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
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Mar 11 2011
STATUS
approved