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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
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
KEYWORD
nonn
AUTHOR
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.)