A397041 Convolution of A000005 and A156616.

0, 1, 4, 12, 35, 90, 222, 518, 1166, 2537, 5372, 11100, 22456, 44570, 86968, 167092, 316533, 591904, 1093686, 1998556, 3614586, 6474608, 11493234, 20229270, 35321450, 61207895, 105307780, 179951412, 305517398, 515507466, 864717152, 1442333294, 2392840112, 3949250852, 6485723990

Offset

0,3

Comments

Convolution of A397040 and A000219.

Convolution of A397039 and A026007.

Links

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

Formula

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

a(n) ~ A156616(n) * 3*n^(1/3) * (log(3*n^(1/3)/(2*r)) + gamma) / (2*r), where r = 3*(7*zeta(3))^(1/3) / 2^(4/3) and gamma is the Euler-Mascheroni constant A001620.

a(n) ~ exp(1/12 + 3*(7*zeta(3))^(1/3) * (n^(2/3) / 2^(4/3))) * (log((2*n/(7*zeta(3)))^(1/3)) + gamma) / (A * 2^(4/9) * sqrt(3*Pi) * (7*zeta(3))^(5/36) * n^(13/36)), where A is the Glaisher-Kinkelin constant (A074962).

Mathematica

nmax = 40; CoefficientList[Series[Sum[x^j/(1-x^j), {j, 1, nmax}] * Product[((1+x^k)/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000005, A156616, A000219, A026007.

Cf. A006128, A305082, A305102.

Cf. A397039, A397040.

Sequence in context: A131593 A119683 A340492 * A084362 A318941 A079736

Adjacent sequences: A397038 A397039 A397040 * A397042 A397043 A397044

Keyword

nonn

Author

Vaclav Kotesovec, Jun 14 2026

Status

approved