A262736 Expansion of Product_{k>=1} (1 + x^(2*k-1))^(2*k-1).

1, 1, 0, 3, 3, 5, 8, 10, 22, 25, 41, 57, 88, 126, 168, 261, 351, 512, 685, 984, 1357, 1865, 2566, 3485, 4838, 6459, 8832, 11831, 16056, 21404, 28660, 38259, 50875, 67613, 89161, 118184, 155321, 204609, 267708, 351125, 458331, 597740, 777590, 1010020, 1310390

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 20.

Formula

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)).

Mathematica

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

Crossrefs

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

Cf. A262924, A285292, A285293.

Sequence in context: A039872 A079965 A285069 * A318684 A336132 A200737

Adjacent sequences: A262733 A262734 A262735 * A262737 A262738 A262739

Keyword

nonn

Author

Vaclav Kotesovec, Sep 29 2015

Status

approved