A000911 a(n) = (2n+3)! /( n! * (n+1)! ).

6, 60, 420, 2520, 13860, 72072, 360360, 1750320, 8314020, 38798760, 178474296, 811246800, 3650610600, 16287339600, 72129646800, 317370445920, 1388495700900, 6044040109800, 26190840475800, 113034153632400, 486046860619320, 2083057974082800, 8900338616535600

Offset

0,1

References

E. R. Hansen, A Table of Series and Products, Prentice-Hall, Englewood Cliffs, NJ, 1975, p. 99.

Links

T. D. Noe, Table of n, a(n) for n = 0..200

Formula

a(n) = 2 * A051133(n+1).

a(n) = A000984(n+1)*A000217(n). - Zerinvary Lajos, May 10 2007

a(n) = 6 * A002802(n). - Zerinvary Lajos, Jun 02 2007

n*a(n) - 2*(2*n+3)*a(n-1) = 0. - R. J. Mathar, Jun 07 2013

G.f.: 6*(1+10*x/( G(0)- 10*x)), where G(k)= 2*x*(2*k+5) + k + 1 - 2*x*(k+1)*(2*k+7)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Jul 14 2013

Sum_{n>=0} (-1)^n/a(n) = 5*A086466-2 = 2*log(phi)*sqrt(5)-2 = 0.1520447... - Jean-François Alcover, Apr 22 2014

From Ilya Gutkovskiy, Jan 31 2017: (Start)

G.f.: 6/(1 - 4*x)^(5/2).

a(n) ~ 2^(2*n+3)*n^(3/2)/sqrt(Pi). (End)

Sum_{n>=0} 1/a(n) = 2 - Pi/sqrt(3) = 2 - A093602. - Amiram Eldar, Oct 13 2020

Example

6 + 60*x + 420*x^2 + 2520*x^3 + 13860*x^4 + 72072*x^5 + 360360*x^6 + ...

Maple

seq(binomial(2*n, n)*binomial(n, (n-2)), n=2..21); # Zerinvary Lajos, May 10 2007

Mathematica

Table[(2 n + 3)!/(n!*(n + 1)!), {n, 0, 20}] (* T. D. Noe, Jun 20 2012 *)

Prog

(PARI) a(n) = 2^(n+4)*polcoeff(pollegendre(n+4), n) /* Ralf Stephan */

Crossrefs

Cf. A000217, A000984, A001801, A002802, A051133, A086466, A093602.

Sequence in context: A259817 A230842 A353039 * A076100 A353040 A269760

Adjacent sequences: A000908 A000909 A000910 * A000912 A000913 A000914

Keyword

nonn

Author

N. J. A. Sloane

Status

approved