A246579 G.f.: x^(k^2)/(mul(1-x^(2*i),i=1..k)*mul(1+x^(2*r-1),r=1..oo)) with k=3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 2, -3, 5, -7, 11, -15, 21, -29, 39, -52, 69, -90, 116, -150, 190, -241, 303, -379, 470, -583, 716, -878, 1071, -1302, 1575, -1902, 2285, -2739, 3273, -3899, 4631, -5489, 6486, -7647, 8996, -10557, 12363, -14450, 16853, -19618, 22798, -26441

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. 2, with k=3.

Crossrefs

k=0,1,2 give (apart perhaps from signs) A081360, A038348, A096778. Cf. A246590.

Programs

Maple

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