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 A144186 Numerators of series expansion of the e.g.f. for the Catalan numbers. 6
 1, 1, 1, 5, 7, 7, 11, 143, 143, 2431, 4199, 4199, 7429, 7429, 7429, 215441, 392863, 392863, 20677, 765049, 765049, 31367009, 58642669, 58642669, 2756205443, 2756205443, 2756205443, 146078888479, 5037203051, 5037203051, 9586934839 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000108, A144187. Sequence in context: A231935 A216835 A033932 * A246458 A153979 A126992 Adjacent sequences:  A144183 A144184 A144185 * A144187 A144188 A144189 KEYWORD nonn,frac,changed AUTHOR Eric W. Weisstein, Sep 13 2008 STATUS approved

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Last modified January 21 17:38 EST 2019. Contains 319350 sequences. (Running on oeis4.)