A246582 G.f.: x^((k^2+k)/2)/(mul(1-x^i,i=1..k)*mul(1+x^r,r=1..oo)) with k = 3.

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

Offset: 0

Author

N. J. A. Sloane, Aug 31 2014

Keywords

• sign

References

• 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.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Crossrefs

For k=0 and 1 we get A081362, A027349 (apart from signs). Cf. A246581, A246583.

Programs

Maple

fSp:=proc(k) local a,i,r;
a:=x^((k^2+k)/2)/mul(1-x^i,i=1..k);
a:=a/mul(1+x^r,r=1..101);
series(a,x,101);
seriestolist(%);
end;
fSp(3);

Mathematica

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 *)

Formula

a(n) ~ (-1)^n * 3^(1/4) * exp(sqrt(n/6)*Pi) / (2^(13/4)*Pi*n^(1/4)). - Vaclav Kotesovec, Mar 12 2016