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A187665 Binomial convolution of the central Lah numbers and the central Stirling numbers of the second kind. 1
1, 3, 47, 1440, 67533, 4280175, 341307292, 32750424588, 3670267277749, 470237282353989, 67781221867781615, 10855095004543985756, 1912103925425230231884, 367398970712627913234708, 76469792506315229551855080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = Sum_{k=0..n} binomial(n,k)*A187535(k)* A048993(2n-2k,n-k).

a(n) ~ c * 16^n * (n-1)!, where c = 0.172113078600558193773... - Vaclav Kotesovec, Jul 05 2021

MAPLE

A048993 := proc(n, k) combinat[stirling2](n, k) ; end proc:

A187535 := proc(n) if n=0 then 1 else binomial(2*n-1, n-1)*(2*n)!/n! end if; end proc:

A187665 := proc(n) add(binomial(n, k)*A187535(k)*A048993(2*n-2*k, n-k), k=0..n) ; end proc:

seq(A187665(n), n=0..10)  ; # R. J. Mathar, Mar 28 2011

MATHEMATICA

L[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]

Table[Sum[Binomial[n, k]L[k]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 14}]

PROG

(Maxima) L(n):= if n=0 then 1 else binomial(2*n-1, n-1)*(2*n)!/n!;

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

CROSSREFS

Sequence in context: A197203 A197801 A239450 * A088718 A219162 A016548

Adjacent sequences:  A187662 A187663 A187664 * A187666 A187667 A187668

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Mar 12 2011

STATUS

approved

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Last modified May 21 05:37 EDT 2022. Contains 353889 sequences. (Running on oeis4.)