A246583 - OEIS

%I #12 Mar 12 2016 15:30:16

%S 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 -20,20,-26,26,-32,37,-41,47,-51,63,-65,78,-81,101,-103,123,-128,155,

%U -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 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 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 Vaclav Kotesovec, <a href="/A246583/b246583.txt">Table of n, a(n) for n = 0..5000</a>

%F 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 fSp:=proc(k) local a,i,r;

%p a:=x^((k^2+k)/2)/mul(1-x^i,i=1..k);

%p a:=a/mul(1+x^r,r=1..101);

%p series(a,x,101);

%p seriestolist(%);

%p end;

%p fSp(4);

%t 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 For k=0 and 1 we get A081362, A027349 (apart from signs). Cf. A246581, A246582.

%K sign

%O 0,15

%A _N. J. A. Sloane_, Aug 31 2014