A187665 Binomial convolution of the central Lah numbers and the central Stirling numbers of the second kind.

1, 3, 47, 1440, 67533, 4280175, 341307292, 32750424588, 3670267277749, 470237282353989, 67781221867781615, 10855095004543985756, 1912103925425230231884, 367398970712627913234708, 76469792506315229551855080

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 A355256 A354556

Adjacent sequences: A187662 A187663 A187664 * A187666 A187667 A187668

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved