OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..423
FORMULA
Product(1/(1-q^n)^(a(n)), n >=1) = sum(A000670(k)*q^k, k>=0).
a(n) ~ n! / (2 * log(2)^(n+1)). - Vaclav Kotesovec, Oct 09 2019
MAPLE
read transforms; A000670 := proc(n) option remember; local k; if n <=1 then 1 else add(binomial(n, k)*A000670(n-k), k=1..n); fi; end; [seq(A000670(i), i=1..30)]; EULERi(%);
# The function EulerInvTransform is defined in A358451.
a := EulerInvTransform(A000670):
seq(a(n), n = 0..22); # Peter Luschny, Nov 21 2022
MATHEMATICA
max = 25; b[0] = 1; b[n_] := b[n] = Sum[Binomial[n, k]*b[n-k], {k, 1, n}]; bb = Array[b, max]; s = {}; For[i=1, i <= max, i++, AppendTo[s, i*bb[[i]] - Sum[s[[d]]*bb[[i-d]], {d, i-1}]]]; a[0] = 1; a[n_] := Sum[If[Divisible[ n, d], MoebiusMu[n/d], 0]*s[[d]], {d, 1, n}]/n; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Feb 25 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mike Zabrocki, Jul 18 2004
EXTENSIONS
a(0)=1 inserted by Alois P. Heinz, Feb 20 2017
STATUS
approved