A277963 G.f.: 1/(1+x) * Product_{k>=1} 1/(1-x^k)^k.

1, 0, 3, 3, 10, 14, 34, 52, 108, 174, 326, 533, 946, 1539, 2628, 4251, 7046, 11288, 18313, 29017, 46261, 72533, 113942, 176841, 274353, 421680, 647065, 985593, 1497641, 2261971, 3406992, 5105317, 7628112, 11346861, 16829094, 24861952, 36623009, 53756775

Offset: 0

Author

Vaclav Kotesovec, Nov 06 2016

Keywords

• nonn

Comments

Convolution of A000219 and A033999.

Links

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

Crossrefs

Cf. A000219, A091360, A087787, A191659.

Programs

Mathematica

CoefficientList[Series[1/(1+x)*Product[1/(1-x^k)^k, {k, 1, 50}], {x, 0, 50}], x]

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k)*A000219(k).

a(n) ~ Zeta(3)^(7/36) * exp(3 * Zeta(3)^(1/3) * (n/2)^(2/3) + 1/12) / (A * sqrt(3*Pi) * 2^(47/36) * n^(25/36)), where A = A074962 is the Glaisher-Kinkelin constant.