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

0,2

Links

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

Example

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 + ...

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 *)

Prog

(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

Crossrefs

Cf. A070933, A010815, A032302.

Sequence in context: A273258 A073124 A278260 * A156717 A198889 A329814

Adjacent sequences: A070874 A070875 A070876 * A070878 A070879 A070880

Keyword

sign

Author

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

Extensions

Edited by Robert G. Wilson v, May 26 2002

Corrected by Vincenzo Librandi, Mar 11 2014

Status

approved