OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..800
FORMULA
Product_{k>=1} (1+x^k)^a(k) = Sum_{n>=0} A000085(n) * x^n.
MAPLE
g:= proc(n) option remember;
`if`(n<2, 1, g(n-1)+(n-1)*g(n-2))
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 < 2, 1, g[n - 1] + (n - 1)*g[n - 2]];
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, Oct 27 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 16 2018
STATUS
approved