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

Author

Omar E. Pol, May 08 2022

Keywords

• nonn

Crossrefs

Partial sums of A210843.

Column 1 of A353690.

Programs

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 *)

PARI

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

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)