A187657 Binomial convolution of the central Stirling numbers of the second kind.

1, 2, 16, 222, 4416, 114660, 3676814, 140408338, 6222858240, 314006546124, 17774855765140, 1115507717954432, 76871991664546170, 5770732305836768712, 468750121409142448386, 40964179307489016777630, 3832326196169482368117760

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