\def\no{\noindent}
\def\sm{\smallskip}

\centerline{The Bernoulli-Carlitz Numbers from $i=2$ to $i=80=3^4-1$ for
${\bf A}={\bf F}_3[T]$.}
\medskip
 
\centerline{David Goss}
\medskip

These computations were put into \TeX\ {\it by  hand} from
some old printouts. The Bernoulli-Carlitz numbers are elements
of ${\bf F}_3(T)$ and are presented in {\it reduced} form. Every effort has
been made to make sure that all is correct, {\it but}...
\bigskip

\no $i=2$ 
$$2 \over T^3+2T$$
\sm

\no $i=4$
$$1 \over T^3+2T$$
\sm

\no $i=6$
$$2 \over T^3+2T$$
\sm

\no $i=8$
$$1 \over T^6+T^4+T^2+1$$
\sm

\no $i=10$ 
$$2T^6+2T^4+2T^2+1 \over T^3+2T$$
\sm

\no $i=12$
$$T^6+T^4+T^2+1 \over T^3+2T$$
\sm 

\no $i=14$
$$2$$
\sm

\no $i=16$
$$T^6+T^4+T^2 \over T^6+T^4+T^2+1$$
\sm

\no $i=18$
$$2T^{12}+T^{10}+2T^6+T^2+2\over T^3+2T$$
\sm

\no $i=20$
$$T^6+T^4+T^2+1$$
\sm

\no $i=22$
$$2T^6+2T^4+2T^2$$
\sm

\no $i=24$
$$T^{12}+2T^{10}+2T^6+T^4 \over T^6+T^4+T^2+1$$
\sm

\no $i=26$
$$2T^{27}+2T^{21}+T^{19}+2T^{15}+T^{13}+T^7 \over
T^{24}+T^{22}+T^{20}+T^{18}+T^{16}+T^{14}+T^{12}+T^{10}+T^8+T^6+T^4+
T^2+1$$
\sm

\no $i=28$
$$T^{42}+T^{40}+T^{38}+2T^{34}+2T^{32}+2T^{30}+2T^{24}+2T^{22}+
2T^{20}+2T^{18}+T^{16}+T^{14}+T^{12}+2T^{10}+2T^2+1\over
T^3+2T$$
\sm

\no $i=30$ 
$$2T^{42}+2T^{40}+2T^{38}+T^{36}+T^{34}+T^{32}+T^{24}+T^{22}+T^{20}+
T^{18}+2T^{16}+2T^{14}+2T^{12}+T^4+T^2+1\over T^3+2T$$
\sm

\no
$i=32$ $$T^{42}+T^{40}+T^{38}+2T^{36}+2T^{34}+2T^{32}+
2T^{24}+2T^{22}+2T^{20}+T^{18}+T^{16}+T^{14}+2T^6+2T^4+2T^2+2\over
T^6+T^4+T^2+1$$
\sm

\no $i=34$ 
$$2T^{36}+T^{28}+2T^{18}+2$$
\sm

\no $i=36$
$$T^{48}+2T^{46}+2T^{42}+T^{38}+T^{34}+2T^{32}+T^{30}+2T^{28}+T^{24}
+2T^{20}+T^{18}+2T^{16}+T^{14}+$$
$$T^{10}+2T^6+2T^2+1$$
$$\rm over$$
$$T^3+2T$$
\sm

\no $i=38$ 
$$2T^{42}+2T^{40}+2T^{38}+T^{36}+T^{34}+T^{32}+2T^{24}+2T^{22}
+2T^{20}+T^{12}+T^{10}+T^8+2T^6+2T^4+2T^2+2$$
\sm

\no $i=40$
$$T^{48}+2T^{46}+T^{42}+2T^{40}+T^{36}+2T^{34}+T^{30}+2T^{28}
+T^{24}+2T^{20}+T^{18}+2T^{14}+T^{12}+2T^8+2T^4+T^2 \over
T^6+T^4+T^2+1$$
\sm

\no $i=42$
$$2T^{42}+2T^{40}+2T^{38}+T^{34}+T^{32}+T^{30}+T^{16}+
T^{14}+T^{12}+2T^8+2T^6+2T^4$$
\sm

\no $i=44$
$$T^{39}+2T^{37}+2T^{33}+T^{31}+2T^{15}+T^{13}+T^9+2T^7$$
\sm

\no $i=46$
$$2T^{48}+T^{46}+2T^{42}+T^{40}+2T^{36}+T^{34}+2T^{24}+
T^{20}+2T^{18}+T^{14}+2T^{12}+T^8$$
\sm

\no $i=48$
$$T^{54}+2T^{36}+2T^{28}+T^{10}\over T^6+T^4+T^2+1$$
\sm

\no $i=50$
$$2T^{45}+T^{39}+T^{37}+2T^{31}+T^{27}+2T^{21}+2T^{19}+T^{13}$$
\sm

\no $i=52$
$$T^{69}+T^{67}+T^{65}+2T^{63}+2T^{61}+2T^{59}+2T^{51}+$$
$$2T^{49}+2T^{47}+T^{39}+T^{37}+T^{35}+T^{27}+T^{25}+T^{23}+2T^{21}+
2T^{19}+2T^{17}$$
$$\rm over$$
$$ T^{24}+T^{22}+T^{20}+T^{18}+T^{16}+T^{14}+
T^{12}+T^{10}+T^8+T^6+T^4+T^2+1$$
\vfill \eject

\no $i=54$ 
$$2T^{84}+T^{82}+2T^{66}+T^{64}+2T^{60}+T^{56}+2T^{48}+T^{46}
+2T^{42}+T^{38}+2T^{36}+T^{28}+2T^{24}+$$
$$T^{20}+2T^{18}+T^2+2$$
$$\rm over$$
$$T^3+2T$$
\sm

\no $i=56$
$$T^{84}+2T^{82}+T^{66}+2T^{64}+2T^{58}+T^{56}+T^{48}+
2T^{46}+2T^{40}+$$
$$T^{38}+T^{30}+2T^{28}+T^{24}+2T^{20}+
T^{18}+T^{16}+T^{14}+T^{12}+T^{10}+T^{8}+T^6+2T^2+1$$
$$\rm over$$
$$T^6+T^4+T^2+1$$
\sm

\no $i=58$
$$2T^{78}+2T^{76}+2T^{74}+T^{72}+2T^{70}+2T^{68}+T^{66}+2T^{64}+2T^{62}
+T^{60}+2T^{58}+2T^{56}+$$ $$T^{54}+2T^{52}+2T^{50}+T^{48}+2T^{46}+
2T^{44}+T^{42}+2T^{40}+2T^{38}+T^{36}+2T^{34}+2T^{32}+T^{30}+
2T^{28}+2T^{26}+T^{24}+2T^{22}+$$ 
$$2T^{20}+2T^{18}+2T^{16}+2T^{14}+2T^{12}+2T^{10}
+2T^8+2T^6+2T^4+2T^2$$
\sm

\no $i=60$
$$T^{78}+T^{76}+T^{74}+T^{72}+T^{70}+T^{68}+T^{66}+T^{64}+T^{62}+
T^{60}+T^{58}+T^{56}+T^{52}+$$ $$T^{50}+T^{48}+T^{46}+T^{44}+T^{42}
+T^{40}+T^{38}+T^{36}+T^{34}+$$ $$T^{32}+T^{30}+T^{26}+T^{24}+T^{22}+
T^{20}+T^{18}+T^{16}+T^{14}+T^{12}+T^{10}+T^8+T^6+T^4$$
\sm

\no $i=62$
$$2T^{75}+T^{73}+2T^{67}+T^{65}+2T^{59}+T^{57}+T^{51}+2T^{47}+$$ $$
T^{43}+2T^{39}+T^{35}+2T^{31}+2T^{25}+T^{23}+2T^{17}+T^{15}+2T^9+T^7$$
\sm

\no $i=64$
$$T^{90}+2T^{84}+2T^{24}+2T^{22}+2T^{20}+T^{18}+2T^{16}+2T^{14}+2T^{10}+2T^8
\over T^6+T^4+T^2+1$$
\sm

\no $i=66$
$$2T^{84}+T^{82}+2T^{78}+2T^{76}+2T^{74}+2T^{72}+2T^{70}
+2T^{68}+$$ $$T^{64}+2T^{62}+ 2T^{58}+T^{56}+2T^{52}+2T^{50}+2T^{48}+2T^{46}+
2T^{44}+2T^{42}+$$ $$T^{38}+2T^{36}+2T^{32}+T^{30}+2T^{26}+2T^{24}+2T^{22}+
2T^{20}+2T^{18}+2T^{16}+T^{12}+2T^{10}$$
\sm

\no $i=68$
$$T^{81}+2T^{63}+2T^{57}+2T^{55}+T^{39}+T^{37}+T^{31}+2T^{13}$$
\sm

\no $i=70$
$$2T^{81}+T^{75}+2T^{73}+T^{67}+2T^{65}+T^{63}+T^{59}+T^{55}+$$ 
$$2T^{51}+T^{47}+
2T^{43}+2T^{39}+2T^{35}+T^{33}+2T^{31}+T^{25}+2T^{23}+T^{17}$$
\vfill \eject

\no $i=72$
$$T^{96}+T^{94}+T^{92}+2T^{90}+2T^{88}+2T^{86}+2T^{78}+2T^{76}+
2T^{74}+T^{72}+2T^{70}+2T^{68}+T^{66}+2T^{64}+$$ $$2T^{62}+2T^{60}+
2T^{52}+2T^{50}+2T^{48}+T^{46}+2T^{44}+2T^{42}+$$ $$T^{40}+2T^{38}
+2T^{36}+2T^{34}+2T^{26}+2T^{24}+2T^{22}+T^{20}+T^{18}+T^{16}$$
$$\rm over$$
$$T^6+T^4+T^2+1$$
\sm

\no $i=74$
$$2T^{87}+2T^{85}+2T^{83}+2T^{81}+2T^{69}+2T^{67}+2T^{65}+2T^{63}+$$
$$T^{61}
+T^{59}+T^{57}+T^{55}+2T^{51}+2T^{49}+2T^{47}+2T^{45}+
T^{43}+T^{41}+T^{39}+T^{37}+T^{25}+T^{23}+$$ $$T^{21}+T^{19}$$
\sm 

\no $i=76$
$$T^{87}+T^{85}+T^{83}+T^{69}+T^{67}+T^{65}+2T^{63}+2T^{61}+$$
$$2T^{59}+T^{51}+T^{49}+T^{47}+2T^{45}+2T^{43}+2T^{41}+2T^{27}+2T^{25}+2T^{23}$$
\sm

\no $i=78$
$$2T^{111}+T^{109}+T^{105}+T^{103}+T^{101}+T^{97}+T^{95}+T^{91}
+$$ $$T^{89}+T^{87}+T^{83}+2T^{81}+T^{57}+2T^{55}+2T^{51}+2T^{49}+2T^{47}+2T^{43}
+2T^{41}+2T^{37}+$$ $$2T^{35}+2T^{33}+2T^{29}+T^{27}$$
$$\rm over$$
$$T^{24}+T^{22}+T^{20}+T^{18}+T^{16}+T^{14}+T^{12}+T^{10}+T^8
+T^6+T^4+T^2+1$$
\sm

\no $i=80$
$$T^{156}+2T^{154}+T^{150}+2T^{148}+T^{144}+2T^{142}+T^{138}+2T^{136}
+2T^{132}+$$ $$T^{128}+2T^{126}+T^{122}+2T^{120}+T^{116}+2T^{114}+T^{110}+
T^{106}+2T^{104}+2T^{102}+$$ $$2T^{100}+2T^{98}+2T^{96}+2T^{94}
+2T^{92}+2T^{90}+2T^{88}+2T^{86}+2T^{84}+$$ $$T^{82}+T^{78}+2T^{74}+T^{72}
+2T^{68}+T^{66}+2T^{62}+T^{60}+2T^{56}+2T^{52}+$$ $$T^{50}+2T^{46}+T^{44}
+2T^{40}+T^{38}+2T^{34}+T^{32}$$
$$\rm over$$
$$T^{72}+T^{64}+T^{56}+T^{48}+T^{40}+T^{32}+T^{24}+T^{16}+T^8+1$$
\end