A394208 Expansion of Product_{k>=1} (1 + x^(k*(3*k-2))) / (1 - x^(k*(3*k-2))).

1, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 6, 6, 6, 6, 8, 10, 10, 10, 10, 12, 14, 14, 16, 18, 18, 18, 18, 22, 26, 26, 28, 30, 30, 30, 30, 34, 38, 38, 42, 46, 48, 50, 50, 54, 58, 58, 64, 70, 74, 78, 78, 82, 86, 86, 92, 98, 102, 106, 106, 114, 122, 124, 132, 140, 146, 150

Offset

0,2

Comments

Convolution of A279281 and A279041.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ Gamma(1 + b/d) * ((4-sqrt(2))*zeta(3/2))^(2/3 + b/(3*d)) * d^(1/6 + b/(3*d)) * exp(3*Pi^(1/3) * ((4-sqrt(2))*zeta(3/2))^(2/3) * (n/d)^(1/3) / 4) / (2^(7/2 + 3*b/(2*d)) * sqrt(3) * Pi^(7/6 - b/(6*d)) * n^(7/6 + b/(3*d))), where d = 3, b = -2.

Mathematica

nmax = 120; CoefficientList[Series[Product[(1 + x^(k*(3*k-2))) / (1 - x^(k*(3*k-2))), {k, 1, Floor[Sqrt[1 + 3*nmax]/3 + 1]}], {x, 0, nmax}], x]

Crossrefs

Cf. A103265, A279281, A279041.

Sequence in context: A166594 A105267 A280263 * A008838 A248783 A244462

Adjacent sequences: A394205 A394206 A394207 * A394209 A394210 A394211

Keyword

nonn

Author

Vaclav Kotesovec, Mar 12 2026

Status

approved