OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..400
FORMULA
O.g.f.: Sum_{n>=1} C(2*n,n)/(n+1) * x^n / Product_{k=0..n} (1-k*x). - Paul D. Hanna, Jul 20 2011
E.g.f.: exp(2*exp(z)-2)*(BesselI(0, 2*exp(z)-2)-BesselI(1, 2*exp(z)-2)). Representation as a sum of an infinite series involving the confluent hypergeometric function 1F1, in Maple notation: a(n)=evalf(sum('k'^n*2^(2*'k')*GAMMA('k'+1/2)*evalf(hypergeom(['k'+1/2], ['k'+2], -4))/(sqrt(Pi)*'k'!*('k'+1)!), 'k'=0..infinity)), n=0, 1...
E.g.f.: hypergeom([1/2], [2], 4*(exp(x)-1)). - Vladeta Jovovic, Sep 11 2003
MAPLE
seq(add(Stirling2(n, k)*binomial(2*k, k)/(k+1), k=0..n), n=0..50); # Robert Israel, Sep 16 2016
MATHEMATICA
Table[Sum[StirlingS2[n, k] Binomial[2k, k]/(k+1), {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Nov 01 2011 *)
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, (2*m)!/(m!*(m+1)!)*x^m/prod(k=1, m, 1-k*x+x*O(x^n))), n)} /* Paul D. Hanna, Jul 20 2011 */
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Karol A. Penson, Oct 08 2001
STATUS
approved