A353689 - OEIS

%I #32 May 11 2022 14:34:01

%S 1,5,18,53,139,333,748,1592,3246,6379,12152,22524,40764,72213,125505,

%T 214378,360473,597450,977196,1578852,2522157,3986658,6239619,9675801,

%U 14874445,22679693,34314378,51539173,76875314,113913453,167741728,245534597,357361857,517293186

%N Convolution of A000716 and the positive integers.

%F From _Vaclav Kotesovec_, May 11 2022: (Start)

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

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

%p a:= proc(n) option remember; `if`(n=0, 1, add(

%p       a(n-j)*(2+3*numtheory[sigma](j)), j=1..n)/n)

%p     end:

%p seq(a(n), n=0..35);  # _Alois P. Heinz_, May 11 2022

%t 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 *)

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

%Y Partial sums of A210843.

%Y Column 1 of A353690.

%K nonn

%O 0,2

%A _Omar E. Pol_, May 08 2022