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