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%I #18 Sep 08 2022 08:45:38
%S 1,1,1,5,7,7,11,143,143,2431,4199,4199,7429,7429,7429,215441,392863,
%T 392863,20677,765049,765049,31367009,58642669,58642669,2756205443,
%U 2756205443,2756205443,146078888479,5037203051,5037203051,9586934839
%N Numerators of series expansion of the e.g.f. for the Catalan numbers.
%H G. C. Greubel, <a href="/A144186/b144186.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>
%F The e.g.f. is Sum_{n >= 0} (x^n/n!)*binomial(2n,n)/(n+1).
%F E.g.f.: exp(2*x)*(BesselI(0, 2*x) - BesselI(1, 2*x)).
%e E.g.f. = 1 + x + x^2 + (5*x^3)/6 + (7*x^4)/12 + ...
%e 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, ...
%p seq(numer(binomial(2*n,n)/(n+1)!),n=0..30); # _Vladeta Jovovic_, Dec 03 2008
%t 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 *)
%o (PARI) vector(30, n, n--; numerator(binomial(2*n,n)/(n+1)!)) \\ _G. C. Greubel_, Jan 17 2019
%o (Magma) [Numerator(Binomial(2*n,n)/Factorial(n+1)): n in [0..30]]; // _G. C. Greubel_, Jan 17 2019
%o (Sage) [numerator(binomial(2*n,n)/factorial(n+1)) for n in (0..30)] # _G. C. Greubel_, Jan 17 2019
%Y Cf. A000108, A144187.
%K nonn,frac
%O 0,4
%A _Eric W. Weisstein_, Sep 13 2008
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