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A144187 Denominators of series expansion of the e.g.f. for the Catalan numbers. 5
1, 1, 1, 6, 12, 20, 60, 1680, 4032, 181440, 907200, 2851200, 17107200, 62270208, 242161920, 29059430400, 232475443200, 1077840691200, 277159034880, 52660216627200, 283555012608000, 65501207912448000, 720513287036928000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 20 04:46 EST 2020. Contains 332063 sequences. (Running on oeis4.)