OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Catalan Number
FORMULA
The e.g.f. is Sum_{n >= 0} (x^n/n!)*binomial(2n,n)/(n+1).
E.g.f.: exp(2*x)*(BesselI(0, 2*x) - BesselI(1, 2*x)).
EXAMPLE
E.g.f. = 1 + x + x^2 + (5*x^3)/6 + (7*x^4)/12 + ...
The coefficients continue like this: 1, 1, 1, 5/6, 7/12, 7/20, 11/60, 143/1680, 143/4032, 2431/181440, 4199/907200, 4199/2851200, 7429/17107200, 7429/62270208, ...
MAPLE
seq(numer(binomial(2*n, n)/(n+1)!), n=0..30); # Vladeta Jovovic, Dec 03 2008
MATHEMATICA
With[{m = 30}, CoefficientList[Series[E^(2*x)*(BesselI[0, 2*x] - BesselI[1, 2*x]), {x, 0, m}], x]]//Numerator (* G. C. Greubel, Jan 17 2019 *)
PROG
(PARI) vector(30, n, n--; numerator(binomial(2*n, n)/(n+1)!)) \\ G. C. Greubel, Jan 17 2019
(Magma) [Numerator(Binomial(2*n, n)/Factorial(n+1)): n in [0..30]]; // G. C. Greubel, Jan 17 2019
(Sage) [numerator(binomial(2*n, n)/factorial(n+1)) for n in (0..30)] # G. C. Greubel, Jan 17 2019
CROSSREFS
KEYWORD
nonn,frac,changed
AUTHOR
Eric W. Weisstein, Sep 13 2008
STATUS
approved