A319859 - OEIS

%I #19 Oct 06 2018 12:57:03

%S 1,1,2,5,11,19,33,63,124,212,350,620,1107,1819,2977,5076,8549,13797,

%T 22199,36304,59271,94406,148948,238199,380653,595930,928696,1460474,

%U 2288948,3541879,5460144,8458886,13084665,20046161,30590724,46871521,71711287,108863135,164802583

%N Expansion of Product_{k>0} (1 + (2*k-1)*x^(2*k-1))/(1 - 2*k*x^(2*k)).

%H Vaclav Kotesovec, <a href="/A319859/b319859.txt">Table of n, a(n) for n = 0..5000</a>

%F From _Vaclav Kotesovec_, Oct 06 2018: (Start)

%F a(n) ~ c * n * 2^(n/2), where

%F c = 59.39385182785860961527832575945047265281719... if n is even

%F c = 59.39502666671757816086328506683601946035153... if n is odd

%F (End)

%p seq(coeff(series(mul((1+(2*k-1)*x^(2*k-1))/(1-2*k*x^(2*k)),k=1..n),x,n+1), x, n), n = 0 .. 40); # _Muniru A Asiru_, Sep 29 2018

%t nmax = 50; CoefficientList[Series[Product[(1 + (2*k-1)*x^(2*k-1))/(1 - 2*k*x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 06 2018 *)

%o (PARI) N=99; x='x+O('x^N); Vec(prod(k=1, N, (1+(2*k-1)*x^(2*k-1))/(1-(2*k)*x^(2*k))))

%Y Cf. A006906, A067553, A282207, A319860.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 29 2018