A187662 Convolution of the (signless) central Lah numbers (A187535) and the central Stirling numbers of the second kind (A007820).

1, 3, 45, 1340, 62133, 3926607, 313159138, 30077004204, 3373855596485, 432604296358341, 62396125789568633, 9997677582465775336, 1761777732880595653932, 338625441643226149909356, 70500059235176885929427760

Offset: 0

Author

Emanuele Munarini, Mar 12 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A187535, A007820.

Programs

Maple

L := n -> if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n! fi;
seq(sum(L(k)*combinat[stirling2](2*(n-k),n-k),k=0..n),n=0..12);

Mathematica

L[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]
Table[Sum[L[k]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 14}]

Maxima

L(n):= if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n!;
makelist(sum(L(k)*stirling2(2*n-2*k,n-k),k,0,n),n,0,12);

Formula

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

a(n) ~ 2^(4*n) * n^n / (exp(n) * sqrt(2*Pi*n)). - Vaclav Kotesovec, May 21 2014