A385012 G.f.: 1/Product_{k>=1} (1 - x^(3*k^2)) * (1 - x^k).

1, 1, 2, 4, 6, 9, 15, 21, 31, 45, 63, 87, 123, 165, 224, 302, 401, 528, 698, 906, 1177, 1520, 1950, 2488, 3173, 4010, 5061, 6363, 7965, 9932, 12366, 15317, 18937, 23342, 28686, 35153, 43002, 52425, 63797, 77454, 93819, 113386, 136807, 164663, 197863, 237302, 284080

Offset

0,3

Links

Table of n, a(n) for n=0..46.

Formula

a(n) ~ exp(Pi*sqrt(2*n/3) + zeta(3/2)*n^(1/4)/(2^(3/4)*3^(1/4)) - zeta(3/2)^2/(32*Pi)) / (2^(13/4) * 3^(1/4) * sqrt(Pi) * n^(5/4)).

Mathematica

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

Crossrefs

Cf. A000041, A001156, A385011.

Sequence in context: A375977 A327046 A024787 * A266648 A076922 A157679

Adjacent sequences: A385009 A385010 A385011 * A385013 A385014 A385015

Keyword

nonn

Author

Vaclav Kotesovec, Jun 15 2025

Status

approved