A353689 Convolution of A000716 and the positive integers.

1, 5, 18, 53, 139, 333, 748, 1592, 3246, 6379, 12152, 22524, 40764, 72213, 125505, 214378, 360473, 597450, 977196, 1578852, 2522157, 3986658, 6239619, 9675801, 14874445, 22679693, 34314378, 51539173, 76875314, 113913453, 167741728, 245534597, 357361857, 517293186

Offset

0,2

Links

Table of n, a(n) for n=0..33.

Formula

From Vaclav Kotesovec, May 11 2022: (Start)

G.f.: 1/(1-x)^2 * Product_{k>=1} 1/(1-x^k)^3.

a(n) ~ exp(Pi*sqrt(2*n)) / (2^(5/2) * Pi^2 * sqrt(n)). (End)

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*(2+3*numtheory[sigma](j)), j=1..n)/n)
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, May 11 2022

Mathematica

nmax = 35; CoefficientList[Series[1/(1 - x)^2 * Product[1/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 11 2022 *)

Prog

(PARI) lista(nn) = Vec(1/(eta('x+O('x^nn))^3*(1-x)^2)); \\ Michel Marcus, May 09 2022

Crossrefs

Partial sums of A210843.

Column 1 of A353690.

Sequence in context: A226903 A056782 A178684 * A271771 A270990 A272558

Adjacent sequences: A353686 A353687 A353688 * A353690 A353691 A353692

Keyword

nonn

Author

Omar E. Pol, May 08 2022

Status

approved