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

0,3

Links

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

Formula

a(n) ~ n^n.

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]

Crossrefs

Cf. A000312, A110143, A326986.

Sequence in context: A331878 A121120 A183681 * A350485 A350109 A185386

Adjacent sequences: A326982 A326983 A326984 * A326986 A326987 A326988

Keyword

nonn

Author

Vaclav Kotesovec, Aug 10 2019

Status

approved