OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..576
FORMULA
Product_{k>=1} (1+x^k)^a(k) = Sum_{n>=0} Bell(n) * x^n.
MAPLE
g:= proc(n) option remember; `if`(n=0, 1,
add(binomial(n-1, j-1)*g(n-j), j=1..n))
end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= proc(n) option remember; g(n)-b(n, n-1) end:
seq(a(n), n=1..30);
MATHEMATICA
g[n_] := g[n] = If[n == 0, 1,
Sum[Binomial[n-1, j-1]*g[n-j], {j, 1, n}]];
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_] := a[n] = g[n] - b[n, n - 1];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Mar 10 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 11 2018
STATUS
approved