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 A187544 Stirling transform (of the second kind) of the central Lah numbers (A187535). 8
 1, 2, 38, 1310, 66254, 4428782, 368444078, 36691056110, 4256199137774, 563672814445742, 83921091641375918, 13875375391723852910, 2522552600160248918894, 500141581330626431059502, 107400097037199576065830958 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 1 22:38 EDT 2023. Contains 365828 sequences. (Running on oeis4.)