A385011 G.f.: 1/Product_{k>=1} (1 - x^(2*k^2)) * (1 - x^k).

1, 1, 3, 4, 8, 11, 19, 26, 42, 57, 86, 116, 168, 224, 314, 415, 568, 743, 998, 1293, 1709, 2196, 2862, 3649, 4702, 5950, 7590, 9540, 12061, 15064, 18895, 23460, 29220, 36081, 44651, 54854, 67490, 82513, 100979, 122904, 149671, 181400, 219904, 265463, 320453, 385397

Offset

0,3

Comments

For n<=17, a(n-1) + a(n) = A369579(n).

Links

Table of n, a(n) for n=0..45.

Formula

a(n) ~ exp(Pi*sqrt(2*n/3) + 3^(1/4)*zeta(3/2)*n^(1/4)/2^(5/4) - 3*zeta(3/2)^2/(64*Pi)) / (2^(11/4) * 3^(3/4) * sqrt(Pi) * n^(5/4)).

Mathematica

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

Crossrefs

Cf. A000041, A001156, A369579, A385012.

Sequence in context: A212549 A212550 A024786 * A299069 A097497 A332681

Adjacent sequences: A385008 A385009 A385010 * A385012 A385013 A385014

Keyword

nonn

Author

Vaclav Kotesovec, Jun 15 2025

Status

approved