A385010 G.f.: Product_{k>=1} (1 + x^(3*k^2)) / (1 - x^k).

1, 1, 2, 4, 6, 9, 14, 20, 29, 41, 57, 78, 108, 144, 193, 257, 338, 441, 575, 741, 953, 1218, 1549, 1960, 2474, 3103, 3882, 4839, 6009, 7435, 9179, 11287, 13847, 16938, 20664, 25143, 30528, 36964, 44667, 53855, 64795, 77792, 93230, 111497, 133113, 158630, 188712

Offset

0,3

Links

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

Formula

a(n) ~ exp(Pi*sqrt(2*n/3) + (sqrt(2) - 1)*zeta(3/2)*n^(1/4)/(2^(5/4)*3^(1/4)) + (2*sqrt(2) - 3)*zeta(3/2)^2/(64*Pi)) / (2^(5/2 )*sqrt(3)*n).

Mathematica

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

Crossrefs

Cf. A000041, A033461, A385009.

Sequence in context: A069916 A153140 A295341 * A139135 A097197 A260600

Adjacent sequences: A385007 A385008 A385009 * A385011 A385012 A385013

Keyword

nonn

Author

Vaclav Kotesovec, Jun 15 2025

Status

approved