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A014322 Convolution of Bell numbers with themselves. 8
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
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
G.f.: ( Sum_{j>=0} A000110(j)*x^j )^2. - G. C. Greubel, Jan 08 2023
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-François Alcover, Jan 17 2016 *)
PROG
(Magma)
A014322:= func< n | (&+[Bell(j)*Bell(n-j): j in [0..n]]) >;
[A014322(n): n in [0..40]]; // G. C. Greubel, Jan 08 2023
(SageMath)
def A014322(n): return sum(bell_number(j)*bell_number(n-j) for j in range(n+1))
[A014322(n) for n in range(41)] # G. C. Greubel, Jan 08 2023
CROSSREFS
Column k=2 of A292870.
Sequence in context: A081558 A202059 A350492 * A095148 A368636 A060996
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified February 26 12:54 EST 2024. Contains 370352 sequences. (Running on oeis4.)