A326985 G.f.: B(x)*B(2*x^2)*B(3*x^3)*..., where B(x) is g.f. of A000312.

1, 1, 6, 32, 287, 3222, 47606, 831488, 16890792, 389286222, 10037183606, 286154919078, 8937624574652, 303483905672078, 11130904101218094, 438532313635906858, 18470060947222927499, 828155619735377936654, 39384843256547964375436, 1980138439071577626157382

Offset: 0

Author

Vaclav Kotesovec, Aug 10 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A000312, A110143, A326986.

Programs

Maple

B:= proc(n) option remember; n^n end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1,
      B(n), add(b(j, 1)*i^j*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 23 2019

Mathematica

nmax = 20; CoefficientList[Series[Product[1+Sum[k^k*j^k*x^(j*k), {k, 1, nmax/j}], {j, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ n^n.