A397056 Convolution of A000203 and A026007.

0, 1, 4, 9, 22, 44, 92, 175, 330, 606, 1076, 1891, 3258, 5526, 9236, 15291, 24964, 40393, 64728, 102791, 161930, 253184, 392978, 605924, 928466, 1414066, 2141696, 3226409, 4835794, 7212968, 10709434, 15830353, 23301798, 34161140, 49887096, 72581655, 105222878, 152017339, 218893288

Offset

0,3

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)^k.

a(n) ~ Pi^(3/2) * exp(3^(4/3)*zeta(3)^(1/3)*n^(2/3)/2^(4/3)) / (9 * 2^(13/12) * zeta(3)^(1/2)).

Mathematica

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

Crossrefs

Cf. A000203, A026007.

Cf. A276432, A397057.

Cf. A066186, A277029, A335651.

Sequence in context: A105314 A200155 A381290 * A382124 A002835 A253289

Adjacent sequences: A397053 A397054 A397055 * A397057 A397058 A397059

Keyword

nonn

Author

Vaclav Kotesovec, Jun 15 2026

Status

approved