login
Expansion of Product_{k>=1} (1 + x^(2*k-1))^(2*k-1).
17

%I #17 Sep 08 2017 06:51:00

%S 1,1,0,3,3,5,8,10,22,25,41,57,88,126,168,261,351,512,685,984,1357,

%T 1865,2566,3485,4838,6459,8832,11831,16056,21404,28660,38259,50875,

%U 67613,89161,118184,155321,204609,267708,351125,458331,597740,777590,1010020,1310390

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

%H Alois P. Heinz, <a href="/A262736/b262736.txt">Table of n, a(n) for n = 0..10000</a>

%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 20.

%F a(n) ~ exp(3^(4/3) * (Zeta(3))^(1/3) * n^(2/3) / 2^(5/3)) * Zeta(3)^(1/6) / (2^(3/4) * 3^(1/3) * sqrt(Pi) * n^(2/3)).

%t nmax = 60; CoefficientList[Series[Product[(1 + x^(2*k-1))^(2*k-1), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A026007, A026011, A255528, A262811, A292038.

%Y Cf. A262924, A285292, A285293.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Sep 29 2015