A246578 Expansion of g.f. (Product_{r>=1} (1 - x^r))*x^(k^2)/Product_{i=1..k} ((1-x^i)^2) with k=4.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 5, 7, 7, 8, 6, 5, 1, -2, -9, -15, -23, -30, -39, -46, -52, -56, -58, -57, -51, -43, -29, -13, 10, 33, 63, 90, 124, 152, 184, 207, 233, 245, 258, 255, 250, 227, 202, 157, 110, 45, -22, -104, -185, -278, -366

Offset: 0

Author

N. J. A. Sloane, Aug 31 2014

Keywords

• sign

Links

• Jason Fulman, 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.

Crossrefs

k=0 gives A010815. Cf. A246575-A246578.

Programs

Maple

fGL:=proc(k) local a,i,r;
a:=x^(k^2)/mul((1-x^i)^2,i=1..k);
a:=a*mul(1-x^r,r=1..101);
series(a,x,101);
seriestolist(%);
end;fGL(4);

Mathematica

With[{k = 4}, CoefficientList[Product[(1-x^r), {r, 1, nmax}]* x^(k^2)/Product[(1-x^i)^2, {i, 1, k}] + O[x]^nmax, x]] (* Jean-François Alcover, Mar 09 2023 *)