|
%I #14 May 14 2021 02:53:16
%S 1,-2,-2,-2,0,6,18,38,68,108,148,148,-2,-552,-2004,-5280,-11960,
%T -24590,-46990,-84254,-141476,-218654,-295794,-295374,3540,1148110,
%U 4378918,12332318,30327568,68633710,146303026,297349758,580052778,1089382158,1969425038,3413378318,5614375970
%N Expansion of Product_{k>=1} ((1 - x)^k - x^k)/((1 - x)^k + x^k).
%F G.f.: theta_4(x/(1 - x)), where theta_4() is the Jacobi theta function.
%t m = 36; CoefficientList[Series[Product[((1 - x)^k - x^k)/((1 - x)^k + x^k), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, May 14 2021 *)
%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-x)^k-x^k)/((1-x)^k+x^k)))
%Y Convolution inverse of A318570.
%Y Cf. A002448, A307521, A307522.
%K sign
%O 0,2
%A _Seiichi Manyama_, Apr 12 2019
|
