OFFSET
1,2
COMMENTS
Representation of a(n) as n-th moment of a positive weight function on a positive half-axis, in Maple notation: a(n)=int(x^n*(1/(48*(Pi)^(3/2)))*exp(-x/32)*BesselK(1,x/32)/sqrt(x), x=0..infinity), n=1,2... .
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
PROG
(PARI) a(n)=(2*n+1)!*(2*n-2)!/((n-1)!*(n!)^2*6); \\ Michel Marcus, Aug 17 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Mar 04 2009
STATUS
approved