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A095993 Inverse Euler transform of the ordered Bell numbers A000670. 4
1, 1, 2, 10, 59, 446, 3965, 41098, 484090, 6390488, 93419519, 1498268466, 26159936547, 494036061550, 10035451706821, 218207845446062, 5057251219268460, 124462048466812950, 3241773988588098756, 89093816361187396674, 2576652694087142999421 (list; graph; refs; listen; history; text; internal format)
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).

MAPLE

See 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(%);

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-Fran├žois Alcover, Feb 25 2017 *)

CROSSREFS

Cf. A000670, A085686, A095989.

Sequence in context: A262910 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

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Last modified August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)