A157713 a(n) = (2*n+1)!*(2*n-2)!/((n-1)!*(n!)^2*6).

1, 10, 280, 12600, 776160, 60540480, 5708102400, 630745315200, 79894406592000, 11408921261337600, 1812981305892556800, 317271728531197440000, 60623305667038033920000, 12557684745315021312000000, 2802875235154312756838400000, 670587900010669327073587200000, 171197146238017934088198144000000

Offset

1,2

Comments

Representation of a(n) as n-th moment of a positive weight function on a positive half-axis: a(n) = Integral_{x=0..oo} x^n*(1/(48*Pi^(3/2)))*exp(-x/32)*BesselK(1,x/32)/sqrt(x) dx, n >= 1.

Links

Table of n, a(n) for n=1..17.

Formula

E.g.f.: (1/12)*(Pi+2*EllipticK(4*sqrt(x))-4*EllipticE(4*sqrt(x)))/Pi

Conjecture: n*a(n) -4*(2*n+1)*(2*n-3)*a(n-1)=0. - R. J. Mathar, Jun 08 2016

a(n) ~ 2^(4*n - 3/2) * n^(n - 1/2) / (3 * sqrt(Pi) * exp(n)). - Vaclav Kotesovec, Jun 26 2022

G.f.: (1-hypergeom([-1/2, 3/2], [], 16*x))/(12*x). - Karol A. Penson, May 20 2025

Prog

(PARI) a(n)=(2*n+1)!*(2*n-2)!/((n-1)!*(n!)^2*6); \\ Michel Marcus, Aug 17 2013

Crossrefs

Sequence in context: A203149 A117654 A067427 * A205824 A251580 A165457

Adjacent sequences: A157710 A157711 A157712 * A157714 A157715 A157716

Keyword

nonn,easy

Author

Karol A. Penson, Mar 04 2009

Extensions

More terms from Michel Marcus, May 02 2025

Status

approved