A187544 Stirling transform (of the second kind) of the central Lah numbers (A187535).

1, 2, 38, 1310, 66254, 4428782, 368444078, 36691056110, 4256199137774, 563672814445742, 83921091641375918, 13875375391723852910, 2522552600160248918894, 500141581330626431059502, 107400097037199576065830958

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Formula

a(n) = sum(S(n,k)*L(k),k=0..n), where S(n,k) are the Stirling numbers of the second kind and L(n) are the central Lah numbers.

E.g.f.: 1/2 + 1/Pi*K(16(exp(x)-1)) where K(z) is the elliptic integral of the first kind (defined as in Mathematica).

a(n) ~ n! / (2*Pi*n * (log(17/16))^n). - Vaclav Kotesovec, Oct 06 2019

Maple

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

Mathematica

a[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]
Table[Sum[StirlingS2[n, k]a[k], {k, 0, n}], {n, 0, 20}]
CoefficientList[Series[1/2 + EllipticK[16*(E^x - 1)]/Pi, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 06 2019 *)

Prog

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

Crossrefs

Cf. A187536, A008297, A111596, A187536, A187538, A187539, A187540, A187542, A187543, A187545, A187546, A187547, A187548.

Sequence in context: A266601 A266597 A291821 * A187545 A246484 A288027

Adjacent sequences: A187541 A187542 A187543 * A187545 A187546 A187547

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 11 2011

Status

approved