A035079 Weigh transform of A007561.

1, 1, 1, 2, 4, 10, 26, 71, 197, 564, 1639, 4833, 14406, 43374, 131652, 402525, 1238419, 3831520, 11912913, 37204431, 116655147, 367100319, 1159026041, 3670339794, 11655070593, 37104257405, 118398974620, 378627600346, 1213247498254, 3894924465243

Offset: 0

Author

Christian G. Bower, Nov 15 1998

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..600
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A035080, A035081.

Programs

Maple

g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(b((i-1)$2), j)*g(n-i*j, i-1), j=0..n/i)))
    end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(g(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> g(n, n):
seq(a(n), n=0..40); # Alois P. Heinz, May 20 2013

Mathematica

g[n_, i_] := g[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[b[i-1, i-1], j]* g[n-i*j, i-1], {j, 0, n/i}]]];
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[g[i, i], j]*b[n- i*j, i-1], {j, 0, n/i}]]];
a[n_] := g[n, n];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 22 2017, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n / n^(3/2), where d = 3.382016466020272807429818743... (same as for A035080), c = 0.2780120087122189647675707... . - Vaclav Kotesovec, Sep 12 2014