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A187657 Binomial convolution of the central Stirling numbers of the second kind. 2
1, 2, 16, 222, 4416, 114660, 3676814, 140408338, 6222858240, 314006546124, 17774855765140, 1115507717954432, 76871991664546170, 5770732305836768712, 468750121409142448386, 40964179307489016777630, 3832326196169482368117760 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) = Sum_{k=0..n} binomial(n,k) * S(2k,k) * S(2n-2k,n-k).

Limit n->infinity (a(n)/n!)^(1/n) = -4/(LambertW(-2*exp(-2))*(2+LambertW(-2*exp(-2)))) = 6.17655460948348... . - Vaclav Kotesovec, Jun 01 2015

MAPLE

seq(sum(binomial(n, k) *combinat[stirling2](2*k, k) *combinat[stirling2](2*(n-k), n-k), k=0..n), n=0..12);

MATHEMATICA

Table[Sum[Binomial[n, k]StirlingS2[2k, k]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 16}]

PROG

(Maxima) makelist(sum(binomial(n, k)*stirling2(2*k, k)*stirling2(2*n-2*k, n-k), k, 0, n), n, 0, 12);

CROSSREFS

Sequence in context: A223638 A188688 A188844 * A047657 A233141 A223631

Adjacent sequences:  A187654 A187655 A187656 * A187658 A187659 A187660

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Mar 12 2011

STATUS

approved

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Last modified January 25 02:37 EST 2022. Contains 350565 sequences. (Running on oeis4.)