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%I #29 Jan 29 2021 23:00:49
%S 1,1,5,16,64,196,661,1921,5431,14106,35006,81858,183616,393568,813916,
%T 1624114,3143974,5910904,10831414,19369614,33887006,58069748,97645340,
%U 161289668,262066349,419245385,661069025,1028234130,1578996010,2395570650,3593235173
%N Molien series for 16-dimensional group of structure Z_2^4.S_3 and order 96, corresponding to complete weight enumerators of Hermitian self-dual GF(4)-linear codes over GF(16) containing 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. See Section 7.6.1, especially Eq. (7.6.16), p. 220.
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%F For the Molien series see the Maple code.
%p f1:= 1 + 4*t^3 + 34*t^4 + 88*t^5 + 237*t^6 + 516*t^7 + 1161*t^8 + 2176*t^9 + 3726*t^10 + 5478*t^11 + 7524*t^12 + 9296*t^13 + 10805*t^14 + 5610 *t^15;
%p f2:=expand(t^30*subs(t=1/t, f1));
%p g:= (1-t)*(1-t^2)^4*(1-t^3)^7*(1-t^4)^4;
%p h:=(f1+f2)/g; # This is the Molien series
%p series(h,t,48); # _N. J. A. Sloane_, Jan 29 2021
%Y Cf. A092496.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Apr 05 2004
%E There were errors in the definition (in the order and structure of the group). The Molien series was correct, but to make it easier to check I replaced the formulas with Maple code. Thanks to _Georg Fischer_ and _Andrey Zabolotskiy_ for noticing that something was wrong. - _N. J. A. Sloane_, Jan 29 2021
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