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A246583 G.f.: x^((k^2+k)/2)/(mul(1-x^i,i=1..k)*mul(1+x^r,r=1..oo)) with k = 4.

%I A246583 #12 Mar 12 2016 15:30:16
%S A246583 0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,-1,2,-2,3,-4,3,-6,5,-9,6,-12,10,-16,13,
%T A246583 -20,20,-26,26,-32,37,-41,47,-51,63,-65,78,-81,101,-103,123,-128,155,
%U A246583 -161,187,-199,232,-247,278,-302,341,-371,407,-449,495,-545,589,-654,711,-786,843,-936,1011,-1116,1194,-1320,1423,-1563,1674
%N A246583 G.f.: x^((k^2+k)/2)/(mul(1-x^i,i=1..k)*mul(1+x^r,r=1..oo)) with k = 4.
%D A246583 Fulman, Jason. Random matrix theory over finite fields. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 51--85. MR1864086 (2002i:60012). See top of page 70, Eq. 3, with k=4.
%H A246583 Vaclav Kotesovec, <a href="/A246583/b246583.txt">Table of n, a(n) for n = 0..5000</a>
%F A246583 a(n) ~ (-1)^n * 3^(3/4) * n^(1/4) * exp(sqrt(n/6)*Pi) / (2^(15/4)*Pi^2). - _Vaclav Kotesovec_, Mar 12 2016
%p A246583 fSp:=proc(k) local a,i,r;
%p A246583 a:=x^((k^2+k)/2)/mul(1-x^i,i=1..k);
%p A246583 a:=a/mul(1+x^r,r=1..101);
%p A246583 series(a,x,101);
%p A246583 seriestolist(%);
%p A246583 end;
%p A246583 fSp(4);
%t A246583 nmax = 100; CoefficientList[Series[x^10/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) * Product[1/(1+x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 11 2016 *)
%Y A246583 For k=0 and 1 we get A081362, A027349 (apart from signs). Cf. A246581, A246582.
%K A246583 sign
%O A246583 0,15
%A A246583 _N. J. A. Sloane_, Aug 31 2014