A095993 Inverse Euler transform of the ordered Bell numbers A000670.

1, 1, 2, 10, 59, 446, 3965, 41098, 484090, 6390488, 93419519, 1498268466, 26159936547, 494036061550, 10035451706821, 218207845446062, 5057251219268460, 124462048466812950, 3241773988588098756, 89093816361187396674, 2576652694087142999421

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

Cf. A000670, A085686, A095989.

Sequence in context: A351502 A202482 A240605 * A029725 A246480 A303361

Adjacent sequences: A095990 A095991 A095992 * A095994 A095995 A095996

Keyword

nonn

Author

Mike Zabrocki, Jul 18 2004

Extensions

a(0)=1 inserted by Alois P. Heinz, Feb 20 2017

Status

approved