A070877 Expansion of Product_{k>=1} (1 - 2x^k).

1, -2, -2, 2, 2, 6, -2, 2, -6, -10, -2, -6, -6, 6, 22, -6, 26, 14, 22, -6, -14, -2, -10, -46, -46, -50, -18, 18, -78, 22, 14, 82, 42, 166, 14, 42, 170, 118, 6, 106, -150, -66, -122, -118, -62, -370, -282, -350, -126, -354, -2, -94, 226, -250, 30, 450, 730, 342, 894, 474, 890, 358, 758, 58, 1210, 782, -778, 26, -270, -1250

Offset: 0

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 24 2002

Keywords

• sign

Examples

			G.f. = 1 - 2*x - 2*x^2 + 2*x^3 + 2*x^4 + 6*x^5 - 2*x^6 + 2*x^7 - 6*x^8 - 10*x^9 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Giovanni Resta)

Crossrefs

Cf. A070933, A010815, A032302.

Programs

Mathematica

CoefficientList[ Series[ Product[(1 - 2t^k), {k, 1, 80}], {t, 0, 80}], t]
a[ n_] := SeriesCoefficient[ -QPochhammer[2, x], {x, 0, n}]; (* Michael Somos, Mar 11 2014 *)

PARI

N=66; q='q+O('q^N); Vec(sum(n=0, N, (-2)^n*q^(n*(n+1)/2) / prod(k=1, n, 1-q^k ) )) \\ Joerg Arndt, Mar 09 2014

PARI

N=66; q='q+O('q^N); t2=Vec( prod(k=1, N, 1-2*q^k) ) \\ Joerg Arndt, Mar 11 2014

Extensions

Edited by Robert G. Wilson v, May 26 2002

Corrected by Vincenzo Librandi, Mar 11 2014