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.

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

Offset

0,15

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=4.

Links

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

Formula

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

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(4);

Mathematica

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 *)

Crossrefs

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

Sequence in context: A003113 A225502 A152227 * A244788 A078660 A239239

Adjacent sequences: A246580 A246581 A246582 * A246584 A246585 A246586

Keyword

sign

Author

N. J. A. Sloane, Aug 31 2014

Status

approved