A089814 Expansion of Product_{k>=1} (1 - q^(10k-5))^2.

1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 5, 0, 0, 0, 0, -6, 0, 0, 0, 0, 9, 0, 0, 0, 0, -12, 0, 0, 0, 0, 13, 0, 0, 0, 0, -16, 0, 0, 0, 0, 21, 0, 0, 0, 0, -26, 0, 0, 0, 0, 29, 0, 0, 0, 0, -36, 0, 0, 0, 0, 46, 0, 0, 0, 0, -54, 0, 0, 0, 0, 62, 0, 0, 0, 0, -74, 0

Offset: 0

Author

Eric W. Weisstein, Nov 12 2003

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A022597 (expansion of Product_{m >= 1} (1 + q^m)^(-2)).

Programs

Magma

m:=100; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1-x^(10*k-5))^2: k in [1..20]]))); // G. C. Greubel, Oct 20 2018

Mathematica

A022597[n_] := SeriesCoefficient[ Product[1 + q^k, {k, n}]^-2, {q, 0, n}]; a[n_] := If[Mod[n, 5] != 0, 0, A022597[n/5]]; a[0] = 1; Table[a[n], {n, 0, 96}] (* Jean-François Alcover, Nov 12 2012, after Michael Somos *)

PARI

x='x+O(x^100); Vec(prod(k=1,20, (1-x^(10*k-5))^2)) \\ G. C. Greubel, Oct 20 2018

Formula

a(5*n) = A022597(n). a(n) = 0 unless n == 0 (mod 5). - Michael Somos, Jun 08 2012