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

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..600

N. J. A. Sloane, Transforms

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

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 *)

Crossrefs

Cf. A035080, A035081.

Sequence in context: A097085 A071962 A257520 * A259206 A106221 A149811

Adjacent sequences: A035076 A035077 A035078 * A035080 A035081 A035082

Keyword

nonn

Author

Christian G. Bower, Nov 15 1998

Status

approved