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%I #13 Mar 09 2023 07:34:24
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,3,5,5,7,7,8,6,5,1,-2,-9,-15,
%T -23,-30,-39,-46,-52,-56,-58,-57,-51,-43,-29,-13,10,33,63,90,124,152,
%U 184,207,233,245,258,255,250,227,202,157,110,45,-22,-104,-185,-278,-366
%N Expansion of g.f. (Product_{r>=1} (1 - x^r))*x^(k^2)/Product_{i=1..k} ((1-x^i)^2) with k=4.
%H Jason Fulman, <a href="https://doi.org/10.1090/S0273-0979-01-00920-X">Random matrix theory over finite fields</a>, Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 51--85. MR1864086 (2002i:60012). See top of page 70.
%p fGL:=proc(k) local a,i,r;
%p a:=x^(k^2)/mul((1-x^i)^2,i=1..k);
%p a:=a*mul(1-x^r,r=1..101);
%p series(a,x,101);
%p seriestolist(%);
%p end;fGL(4);
%t With[{k = 4}, CoefficientList[Product[(1-x^r), {r, 1, nmax}]* x^(k^2)/Product[(1-x^i)^2, {i, 1, k}] + O[x]^nmax, x]] (* _Jean-François Alcover_, Mar 09 2023 *)
%Y k=0 gives A010815. Cf. A246575-A246578.
%K sign
%O 0,19
%A _N. J. A. Sloane_, Aug 31 2014
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