%I #10 Jan 25 2021 10:29:08

%S 1,1,7,21,92,291,981,2871,8134,21131,52481,122759,275356,590289,

%T 1220811,2436045,4715827,8866230,16246890,29054190,50830264,87104226,

%U 146467614,241934106,393098860,628867434,991602894,1542350194,2368492984,3593354974

%N Molien series for complete weight enumerators of trace-additive Hermitian self-dual codes over the Galois ring GR(4,2) that contain the all-ones vector.

%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.

%H <a href="/index/Mo#Molien">Index entries for Molien series</a>

%F G.f.: u1/u2 where u1 := f(t) + t^41*f(1/t), u2 := (1-t)*(1-t^2)^6*(1-t^4)^7*(1-t^8)^2 and

%F f(t) := 1 + 14*t^3 + 43*t^4 + 115*t^5 + 334*t^6 + 808*t^7 + 1752*t^8 + 3557*t^9 + 6448*t^10 + 10800*t^11 + 17020*t^12 + 24972*t^13 + 34704*t^14 + 45824*t^15 + 57298*t^16 + 68464*t^17 + 78120*t^18 + 85092*t^19 + 88922*t^20.

%p f := 1 + 14*t^3 + 43*t^4 + 115*t^5 + 334*t^6 + 808*t^7 + 1752*t^8 + 3557*t^9 + 6448*t^10 + 10800*t^11 + 17020*t^12 + 24972*t^13 + 34704*t^14 + 45824*t^15 + 57298*t^16 + 68464*t^17 + 78120*t^18 + 85092*t^19 + 88922*t^20;

%p u1 := f + t^41*subs(t=1/t,f); u2 := (1-t)*(1-t^2)^6*(1-t^4)^7*(1-t^8)^2;

%p seq(coeff(series(u1/u2, t, n+1), t, n), n = 0..45); # _Georg Fischer_, Jan 25 2021

%K nonn

%O 0,3

%A G. Nebe (nebe(AT)math.rwth-aachen.de), Nov 10, 2004