A246582 - OEIS

%I #12 Mar 12 2016 15:15:51

%S 0,0,0,0,0,0,1,0,1,0,1,-1,1,-2,1,-3,1,-4,2,-5,3,-6,5,-7,7,-8,10,-10,

%T 13,-12,17,-15,21,-19,26,-24,31,-30,38,-38,45,-47,54,-58,64,-71,77,

%U -86,91,-103,109,-124,129,-147,154,-174,182,-205,216,-241,254,-282,300,-330,351,-384,412,-447,480,-519,560,-602,649,-696,753,-805

%N G.f.: x^((k^2+k)/2)/(mul(1-x^i,i=1..k)*mul(1+x^r,r=1..oo)) with k = 3.

%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=3.

%H Vaclav Kotesovec, <a href="/A246582/b246582.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) ~ (-1)^n * 3^(1/4) * exp(sqrt(n/6)*Pi) / (2^(13/4)*Pi*n^(1/4)). - _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(3);

%t nmax = 100; CoefficientList[Series[x^6/((1-x)*(1-x^2)*(1-x^3)) * 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, A246583.

%K sign

%O 0,14

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