A396891 Convolution of A001157 and A000219.

0, 1, 6, 18, 52, 120, 288, 602, 1280, 2538, 5000, 9449, 17748, 32305, 58338, 103185, 180752, 311678, 532818, 899270, 1505560, 2494674, 4102450, 6688009, 10828656, 17400825, 27787370, 44081766, 69530552, 109028748, 170068890, 263881579, 407469728, 626174109, 957982470, 1459186610

Offset

0,3

Links

Table of n, a(n) for n=0..35.

Formula

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

a(n) ~ zeta(3)^(7/36) * exp(1/12 + 3*zeta(3)^(1/3)*n^(2/3)/2^(2/3)) * n^(11/36) / (A * 2^(11/36) * sqrt(3*Pi)), where A is the Glaisher-Kinkelin constant (A074962).

Mathematica

nmax = 40; CoefficientList[Series[Sum[j^2*x^j/(1-x^j), {j, 1, nmax}] / Product[(1-x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A001157, A000219, A074962, A276432.

Sequence in context: A075650 A015645 A001216 * A396199 A318484 A079843

Adjacent sequences: A396888 A396889 A396890 * A396892 A396893 A396894

Keyword

nonn

Author

Vaclav Kotesovec, Jun 09 2026

Status

approved