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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..600
- N. J. A. Sloane, Transforms
Programs
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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
Comments