OFFSET
1,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..600
N. J. A. Sloane, Transforms
FORMULA
Shifts left under Weigh transform.
a(n) ~ c * d^n / n^(3/2), where d = 3.3683668081969694736300401764..., c = 0.4229796097587478606873477... . - Vaclav Kotesovec, Sep 10 2014
G.f. A(x) satisfies: A(x) = x + x * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) / k ). - Ilya Gutkovskiy, May 19 2023
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n<2, 2*n, b(n-1, n-1)):
seq(a(n), n=1..35); # Alois P. Heinz, Aug 01 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*b[n- i*j, i-1], {j, 0, n/i}]]];
a[n_] := If[n<2, 2*n, b[n-1, n-1]];
Table[a[n], {n, 1, 35}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 04 1999
STATUS
approved