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 A003409 a(n) = 3*binomial(2n-1,n). (Formerly M2814) 8
 3, 9, 30, 105, 378, 1386, 5148, 19305, 72930, 277134, 1058148, 4056234, 15600900, 60174900, 232676280, 901620585, 3500409330, 13612702950, 53017895700, 206769793230, 807386811660, 3156148445580, 12350146091400, 48371405524650, 189615909656628, 743877799422156 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..200 C. Domb and A. J. Barrett, Enumeration of ladder graphs, Discrete Math. 9 (1974), 341-358. C. Domb & A. J. Barrett, Enumeration of ladder graphs, Discrete Math. 9 (1974), 341-358. (Annotated scanned copy) C. Domb & A. J. Barrett, Notes on Table 2 in "Enumeration of ladder graphs", Discrete Math. 9 (1974), 55. (Annotated scanned copy) FORMULA a(n) = (3/2)*4^n*Gamma(1/2+n)/(sqrt(Pi)*Gamma(1+n)). - Peter Luschny, Dec 14 2015 From Stefano Spezia, Jul 05 2021: (Start) O.g.f.: 6*x/((1 - sqrt(1 - 4*x))*sqrt(1 - 4*x)) - 3. E.g.f.: 3*(exp(2*x)*I_0(2*x) - 1)/2, where I_n(x) is the modified Bessel function of the first kind. a(n) ~ 3*4^n/(2*sqrt(n*Pi)). (End) MAPLE a := n -> (3/2)*4^n*GAMMA(1/2+n)/(sqrt(Pi)*GAMMA(1+n)): seq(a(n), n=1..26); # Peter Luschny, Dec 14 2015 MATHEMATICA Table[3*Binomial[2*n - 1, n], {n, 20}] (* T. D. Noe, Oct 07 2013 *) PROG (PARI) a(n) = 3*binomial(2*n-1, n) \\ Charles R Greathouse IV, Oct 23 2023 CROSSREFS Equals 3 * A001700. Sequence in context: A339036 A360715 A029651 * A316371 A181933 A148957 Adjacent sequences: A003406 A003407 A003408 * A003410 A003411 A003412 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Jon E. Schoenfield, Mar 26 2010 STATUS approved

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Last modified April 24 05:26 EDT 2024. Contains 371918 sequences. (Running on oeis4.)