A187546 Stirling transform (of the first kind, with signs) of the central Lah numbers (A187535).

1, 2, 34, 1096, 51984, 3262488, 254943384, 23853046656, 2600024557248, 323588157732096, 45276442446814656, 7035574740347812800, 1202158966644148296000, 224022356544364922931840, 45215509996613004825121920

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: A227935 A264669 A367510 * A195005 A215957 A171732

Adjacent sequences: A187543 A187544 A187545 * A187547 A187548 A187549

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 11 2011

Status

approved