A262924 Expansion of Product_{k>=1} (1 + x^(3*k-1))^(3*k-1) * (1 + x^(3*k-2))^(3*k-2).

1, 1, 2, 2, 5, 10, 13, 25, 35, 57, 87, 134, 211, 306, 458, 684, 996, 1465, 2129, 3073, 4411, 6288, 8977, 12707, 17913, 25185, 35231, 49078, 68228, 94490, 130408, 179425, 246121, 336681, 459239, 624842, 847986, 1147728, 1549773, 2087972, 2806455, 3764136

Offset

0,3

Comments

Convolution of A262948 and A262949.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vaclav Kotesovec)

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

Formula

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

Mathematica

nmax=60; CoefficientList[Series[Product[(1 + x^(3*k-1))^(3*k-1)*(1 + x^(3*k-2))^(3*k-2), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A262884, A262878, A262879, A262923, A261612, A262928, A262948, A262949.

Cf. A262736, A285292, A285293.

Sequence in context: A223062 A208788 A246864 * A331540 A329676 A247354

Adjacent sequences: A262921 A262922 A262923 * A262925 A262926 A262927

Keyword

nonn

Author

Vaclav Kotesovec, Oct 04 2015

Status

approved