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

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..480

Eric Weisstein's World of Mathematics, Catalan Number

Formula

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 + ...

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 *)

Prog

(PARI) vector(30, n, n--; denominator(binomial(2*n, n)/(n+1)!)) \\ G. C. Greubel, Jan 17 2019
(Magma) [Denominator(Binomial(2*n, n)/Factorial(n+1)): n in [0..30]]; // 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

Crossrefs

Cf. A000108, A144186.

Sequence in context: A028611 A220470 A141808 * A303481 A247256 A292951

Adjacent sequences: A144184 A144185 A144186 * A144188 A144189 A144190

Keyword

nonn,frac

Author

Eric W. Weisstein, Sep 13 2008

Status

approved