A374018 Expansion of Product_{k>=1} 1 / (1 - x^(3*k-1))^2.

1, 0, 2, 0, 3, 2, 4, 4, 7, 6, 13, 10, 19, 18, 27, 30, 42, 44, 63, 66, 91, 100, 130, 144, 187, 206, 263, 294, 364, 412, 506, 568, 696, 782, 943, 1070, 1273, 1444, 1713, 1936, 2285, 2586, 3027, 3428, 3996, 4516, 5243, 5924, 6841, 7730, 8895, 10030, 11512, 12966, 14825, 16696

Offset

0,3

Links

Table of n, a(n) for n=0..55.

Formula

a(0) = 1; a(n) = (2/n) * Sum_{k=1..n} A078182(k) * a(n-k).

a(n) = Sum_{k=0..n} A035386(k) * A035386(n-k).

a(n) ~ exp(2*Pi*sqrt(n)/3) * Pi^(4/3) / (3^(3/2) * Gamma(1/3)^2 * n^(11/12)). - Vaclav Kotesovec, Jun 25 2024

Mathematica

nmax = 55; CoefficientList[Series[Product[1/(1 - x^(3 k - 1))^2, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000712, A022567, A035386, A078182, A261616, A374019.

Sequence in context: A008807 A263149 A008819 * A279591 A279675 A169646

Adjacent sequences: A374015 A374016 A374017 * A374019 A374020 A374021

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 25 2024

Status

approved