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 A187545 Stirling transform (of the first kind) of the central Lah numbers (A187535). 8
 1, 2, 38, 1312, 66408, 4442088, 369791064, 36848702784, 4277191653888, 566809715422464, 84441103242634176, 13970100487593468480, 2541362625439551554880, 504185908064687887996800, 108336183242510523080868480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n) = sum(s(n,k)*L(k), k=0..n), where s(n,k) are the (signless) Stirling numbers of the first kind and L(n) are the central Lah numbers. E.g.f.: 1/2 + 1/Pi*K(-16*log(1-x)), where K(z) is the elliptic integral of the first kind (defined as in Mathematica). a(n) ~ n! / (2*Pi*n * (1 - exp(-1/16))^n). - Vaclav Kotesovec, Apr 10 2018 MAPLE lahc := n -> if n=0 then 1 else binomial(2*n-1, n-1)*(2*n)!/n! fi; seq(add(abs(combinat[stirling1](n, k))*lahc(k), k=0..n), n=0..20); MATHEMATICA lahc[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!] Table[Sum[Abs[StirlingS1[n, k]]*lahc[k], {k, 0, n}], {n, 0, 20}] PROG (Maxima) lahc(n):= if n=0 then 1 else binomial(2*n-1, n-1)*(2*n)!/n!; makelist(sum(abs(stirling1(n, k))*lahc(k), k, 0, n), n, 0, 12); CROSSREFS Cf. A187536, A008297, A111596, A187536, A187538, A187539, A187540, A187542, A187543, A187544, A187546, A187547, A187548. Sequence in context: A266597 A291821 A187544 * A246484 A288027 A184994 Adjacent sequences: A187542 A187543 A187544 * A187546 A187547 A187548 KEYWORD nonn,easy,nice AUTHOR Emanuele Munarini, Mar 11 2011 STATUS approved

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Last modified December 11 07:17 EST 2023. Contains 367717 sequences. (Running on oeis4.)