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A187546 Stirling transform (of the first kind, with signs) of the central Lah numbers (A187535). 8
1, 2, 34, 1096, 51984, 3262488, 254943384, 23853046656, 2600024557248, 323588157732096, 45276442446814656, 7035574740347812800, 1202158966644148296000, 224022356544364922931840, 45215509996613004825121920 (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((-1)^(n-k)*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 * (exp(1/16) - 1)^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(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[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(stirling1(n, k)*lahc(k), k, 0, n), n, 0, 12);

CROSSREFS

Cf. A187536, A008297, A111596, A187536, A187538, A187539, A187540, A187542, A187543, A187544, A187545, A187547, A187548.

Sequence in context: A224882 A227935 A264669 * A195005 A215957 A171732

Adjacent sequences:  A187543 A187544 A187545 * A187547 A187548 A187549

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Mar 11 2011

STATUS

approved

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Last modified December 7 04:21 EST 2021. Contains 349567 sequences. (Running on oeis4.)