OFFSET
0,1
COMMENTS
a(n) = 6*A002802(n). - Zerinvary Lajos, Jun 02 2007
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
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). - 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
with(combinat):a:=n->sum(sum(numbcomp(2*n, n), j=2..n), k=1..n): seq(a(n), 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
KEYWORD
nonn
AUTHOR
STATUS
editing