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A256006 Recurrence: a(n) = Sum_{k=0..n-1} a(k)*C(n+1,k), a(0)=1. 2
1, 1, 4, 29, 336, 5687, 132294, 4047969, 157601068, 7607093435, 445794008034, 31177310522789, 2564976392355144, 245223349515360543, 26959450820298057694, 3377267272710103354409, 478240674001176206987556, 76011318838172580152245187 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The number of merger histories for n+1 distinct firms into one firm, where any number of firms may be merged at a time but mergers of two separate sets of firms never occur simultaneously. See MathStackExchange link. - William P. Orrick, Oct 28 2016

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..260

Christian Blatter, How many ways to merge N companies into one big company: Bell or Catalan?, Math StackExchange.

FORMULA

a(n) ~ c * n^(2*n+8/3) / (2^n * exp(2*n)), where c = 4.001655169623968944922713533374039000521095549333460838578... .

MATHEMATICA

nmax = 30; aa = ConstantArray[0, nmax+1]; aa[[1]] = 1; Do[aa[[n+1]]=Sum[Binomial[n+1, k]*aa[[k+1]], {k, 0, n-1}], {n, nmax}]; aa

CROSSREFS

Cf. A103996.

Sequence in context: A099700 A305636 A276728 * A137646 A231498 A168602

Adjacent sequences:  A256003 A256004 A256005 * A256007 A256008 A256009

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, May 06 2015

STATUS

approved

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Last modified May 16 15:56 EDT 2022. Contains 353706 sequences. (Running on oeis4.)