A187664 Convolution of the (signless) central Lah numbers (A187535) and the (signless) central Stirling numbers of the first kind (A187646).

1, 3, 49, 1483, 67615, 4173203, 326208269, 30880075203, 3430574739759, 437145190334383, 62803806114813801, 10038354053796477099, 1766255133182030548351, 339166069936077378326187, 70571377417819411767223541

Offset

0,2

Links

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

Formula

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

a(n) ~ 2^(4*n - 1/2) * n^(n - 1/2) / (sqrt(Pi) * exp(n)). - Vaclav Kotesovec, May 30 2025

Maple

L := n -> if n=0 then 1 else binomial(2*n-1, n-1)*(2*n)!/n! fi;
seq(sum(L(k)*abs(combinat[stirling1](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]Abs[StirlingS1[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(L(k)*abs(stirling1(2*n-2*k, n-k)), k, 0, n), n, 0, 12);

Crossrefs

Cf. A187535, A187646.

Sequence in context: A302466 A303248 A369942 * A380754 A336673 A012199

Adjacent sequences: A187661 A187662 A187663 * A187665 A187666 A187667

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved