A319859 Expansion of Product_{k>0} (1 + (2*k-1)*x^(2*k-1))/(1 - 2*k*x^(2*k)).
1, 1, 2, 5, 11, 19, 33, 63, 124, 212, 350, 620, 1107, 1819, 2977, 5076, 8549, 13797, 22199, 36304, 59271, 94406, 148948, 238199, 380653, 595930, 928696, 1460474, 2288948, 3541879, 5460144, 8458886, 13084665, 20046161, 30590724, 46871521, 71711287, 108863135, 164802583
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..5000
Programs
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Maple
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
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Mathematica
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 *) -
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))))
Formula
From Vaclav Kotesovec, Oct 06 2018: (Start)
a(n) ~ c * n * 2^(n/2), where
c = 59.39385182785860961527832575945047265281719... if n is even
c = 59.39502666671757816086328506683601946035153... if n is odd
(End)