A326986 G.f.: B(x)*B(x^2)*B(x^3)*..., where B(x) is g.f. of A000312.

1, 1, 5, 29, 266, 3163, 46994, 827107, 16828741, 388308078, 10017853262, 285720195351, 8926575094978, 303172417424680, 11121259586618456, 438207141286916539, 18458204444260001120, 827690809585441201775, 39365349178064541861252, 1979267564496263599093676

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)*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*x^(j*k), {k, 1, nmax/j}], {j, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000312, A096161, A309652, A326985.

Sequence in context: A342449 A345098 A144015 * A228387 A181356 A177440

Adjacent sequences: A326983 A326984 A326985 * A326987 A326988 A326989

Keyword

nonn

Author

Vaclav Kotesovec, Aug 10 2019

Status

approved