A246580 G.f.: x^(k^2)/(mul(1-x^(2*i),i=1..k)*mul(1+x^(2*r-1),r=1..oo)) with k=4.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 2, -3, 5, -7, 11, -15, 22, -30, 41, -55, 74, -97, 127, -165, 212, -271, 344, -434, 544, -680, 843, -1043, 1283, -1573, 1919, -2336, 2829, -3419, 4116, -4942, 5914, -7062, 8405, -9983, 11825, -13976, 16479, -19392, 22767

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=4.

Crossrefs

k=0,1,2 give (apart perhaps from signs) A081360, A038348, A096778. Cf. A246589.

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(4);