A070877 - OEIS

%I #31 Sep 09 2017 07:05:17

%S 1,-2,-2,2,2,6,-2,2,-6,-10,-2,-6,-6,6,22,-6,26,14,22,-6,-14,-2,-10,

%T -46,-46,-50,-18,18,-78,22,14,82,42,166,14,42,170,118,6,106,-150,-66,

%U -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

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

%H Seiichi Manyama, <a href="/A070877/b070877.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Giovanni Resta)

%e 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 + ...

%t CoefficientList[ Series[ Product[(1 - 2t^k), {k, 1, 80}], {t, 0, 80}], t]

%t a[ n_] := SeriesCoefficient[ -QPochhammer[2, x], {x, 0, n}]; (* _Michael Somos_, Mar 11 2014 *)

%o (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

%o (PARI) N=66; q='q+O('q^N); t2=Vec( prod(k=1, N, 1-2*q^k) ) \\ _Joerg Arndt_, Mar 11 2014

%Y Cf. A070933, A010815, A032302.

%K sign

%O 0,2

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

%E Edited by _Robert G. Wilson v_, May 26 2002

%E Corrected by _Vincenzo Librandi_, Mar 11 2014