A281781 - OEIS

%I #21 May 29 2018 00:47:03

%S 1,1,-1,2,-1,-2,6,-6,3,-1,-1,9,-18,23,-27,23,-1,-24,49,-89,121,-117,

%T 96,-60,-18,138,-275,408,-525,592,-566,444,-181,-276,854,-1485,2154,

%U -2765,3157,-3131,2571,-1468,-301,2813,-5860,9153,-12386,15082,-16664,16558,-14125

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

%H Seiichi Manyama, <a href="/A281781/b281781.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: exp(Sum_{k>=1} x^k/(k*(1 + x^k)^2)). - _Ilya Gutkovskiy_, May 28 2018

%t nmax = 50; CoefficientList[Series[Product[(1 - x^(2*k))^(2*k)/(1 - x^(2*k-1))^(2*k-1), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 09 2017 *)

%t nmax = 50; CoefficientList[Series[Product[(1 - x^(2*k))^(4*k)/(1 - x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 09 2017 *)

%t nmax = 50; CoefficientList[Series[Product[(1 + x^k)^(4*k)*(1 - x^k)^(3*k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 09 2017 *)

%o (PARI) x='x+O('x^51); Vec(prod(k=1, 50, (1 - x^(2*k))^(2*k)/(1 - x^(2*k-1))^(2*k-1))) \\ _Indranil Ghosh_, Apr 14 2017

%Y Cf. A262811, A281683.

%K sign

%O 0,4

%A _Seiichi Manyama_, Apr 14 2017