A397057 Convolution of A000203 and A156616.

0, 1, 5, 16, 49, 130, 332, 792, 1825, 4049, 8726, 18320, 37620, 75682, 149564, 290788, 557017, 1052590, 1964353, 3623568, 6612698, 11946904, 21381720, 37930772, 66730680, 116478135, 201805078, 347179864, 593284716, 1007389494, 1700141724, 2852620740, 4759740593, 7899577736, 13043665078

Offset

0,3

Comments

Convolution of A276432 and A026007.

Convolution of A397056 and A000219.

Links

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

Formula

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

a(n) ~ Pi^(3/2) * exp(1/12 + 3*(7*zeta(3))^(1/3)*n^(2/3)/2^(4/3)) / (A * 2^(10/9) * 3^(3/2) * (7*zeta(3))^(17/36) * n^(1/36)), where A is the Glaisher-Kinkelin constant A074962.

Mathematica

nmax = 50; CoefficientList[Series[Sum[j*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. A000203, A000219, A026007, A156616.

Cf. A276432, A397056.

Cf. A066186, A277029, A335651.

Sequence in context: A166868 A055144 A171426 * A180129 A244410 A052909

Adjacent sequences: A397054 A397055 A397056 * A397058 A397059 A397060

Keyword

nonn

Author

Vaclav Kotesovec, Jun 15 2026

Status

approved