A092545 - OEIS

%I #11 Feb 02 2020 22:25:38

%S 1,3,44,361,2010,7952,25401,68662,164459,357241,718934,1357271,

%T 2431460,4164014,6864051,10942908,16946805,25576479,37731200,54532437,

%U 77381198,107985724,148434413,201227282,269366687,356392309,466492202,604540771

%N Molien series for complete weight enumerators of self-dual codes over Z/8Z containing the all-ones vector.

%H G. C. Greubel, <a href="/A092545/b092545.txt">Table of n, a(n) for n = 0..1000</a>

%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 := subs(x=x^8, f); f := 1 + 35*x^2 + 237*x^3 + 943*x^4 + 2250*x^5 + 4089*x^6 + 5659*x^7 + 6323*x^8 + 5680*x^9 + 4057*x^10 + 2311*x^11 + 909*x^12 + 246*x^13 + 27*x^14 + x^15; u2 := (1-x^8)^3*(1-x^16 )^3*(1-x^32 )^2.

%p f(x):= (1 +35*x^2 +237*x^3 +943*x^4 +2250*x^5 +4089*x^6 +5659*x^7 +6323*x^8 +5680*x^9 +4057*x^10 +2311*x^11 +909*x^12 +246*x^13 + 27*x^14 +x^15)/((1-x)^3*(1-x^2)^3*(1-x^4)^2);

%p seq(coeff(series( f(x), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Feb 02 2020

%t CoefficientList[Series[(1 +35*x^2 +237*x^3 +943*x^4 +2250*x^5 +4089*x^6 +5659*x^7 +6323*x^8 +5680*x^9 +4057*x^10 +2311*x^11 +909*x^12 +246*x^13 + 27*x^14 +x^15)/((1-x)^3*(1-x^2)^3*(1-x^4)^2), {x,0,30}], x] (* _G. C. Greubel_, Feb 02 2020 *)

%Y Cf. A092544, A092545, A092546, A092547.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Apr 09 2004