A144187 Denominators of series expansion of the e.g.f. for the Catalan numbers.

1, 1, 1, 6, 12, 20, 60, 1680, 4032, 181440, 907200, 2851200, 17107200, 62270208, 242161920, 29059430400, 232475443200, 1077840691200, 277159034880, 52660216627200, 283555012608000, 65501207912448000, 720513287036928000

Offset: 0

Author

Eric W. Weisstein, Sep 13 2008

Keywords

• nonn
• frac

Examples

			E.g.f. = 1 + x + x^2 + (5*x^3)/6 + (7*x^4)/12 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..480
• Eric Weisstein's World of Mathematics, Catalan Number

Crossrefs

Cf. A000108, A144186.

Programs

Magma

[Denominator(Binomial(2*n,n)/Factorial(n+1)): n in [0..30]]; // G. C. Greubel, Jan 17 2019

Maple

seq(denom(binomial(2*n,n)/(n+1)!),n=0..30); # Vladeta Jovovic, Dec 03 2008

Mathematica

With[{m = 30}, CoefficientList[Series[Exp[2*x]*(BesselI[0, 2*x] - BesselI[1, 2*x]), {x, 0, m}], x]]//Denominator (* G. C. Greubel, Jan 17 2019 *)

PARI

vector(30, n, n--; denominator(binomial(2*n,n)/(n+1)!)) \\ G. C. Greubel, Jan 17 2019

Sage

[denominator(binomial(2*n,n)/factorial(n+1)) for n in (0..30)] # G. C. Greubel, Jan 17 2019

Formula

E.g.f.: exp(2*x)*(BesselI(0, 2*x) - BesselI(1, 2*x)).