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A014322 Convolution of Bell numbers with themselves. 4
1, 2, 5, 14, 44, 154, 595, 2518, 11591, 57672, 308368, 1762500, 10716321, 69011130, 468856113, 3348695194, 25064539520, 196052415230, 1598543907843, 13556379105766, 119332020447219, 1088376385244908, 10268343703117892, 100063762955374568, 1005822726810785809 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals row sums of triangle A144155. - Gary W. Adamson, Sep 12 2008

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..576

Adam M. Goyt and Lara K. Pudwell, Avoiding colored partitions of two elements in the pattern sense, arXiv preprint arXiv:1203.3786 [math.CO], 2012. - From N. J. A. Sloane, Sep 17 2012

FORMULA

G.f.: (1/(1 - x - x^2/(1 - 2*x - 2*x^2/(1 - 3*x - 3*x^2/(1 - 4*x - 4*x^2/(1 - ...))))))^2, a continued fraction. - Ilya Gutkovskiy, Sep 25 2017

MAPLE

with(combinat):

a:= n-> add(bell(i)*bell(n-i), i=0..n):

seq(a(n), n=0..30);  # Alois P. Heinz, May 13 2014

MATHEMATICA

a[n_] := Sum[BellB[k] BellB[n-k], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Jan 17 2016 *)

CROSSREFS

Cf. A000110.

Cf. A144155. - Gary W. Adamson, Sep 12 2008

Column k=2 of A292870.

Sequence in context: A204064 A081558 A202059 * A095148 A060996 A134378

Adjacent sequences:  A014319 A014320 A014321 * A014323 A014324 A014325

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 15 12:38 EDT 2019. Contains 327078 sequences. (Running on oeis4.)