OFFSET
1,1
COMMENTS
Representation as n-th moment of a positive function on a positive half-axis, related to the generalized hypergeometric function 0F2: a(n)=integral {x=0..infinity} x^n* 2*sqrt(x)* K_{1}(2*sqrt(x))* 0F2( ; 2,2; x)/exp(1) dx, where K is a modified Bessel function.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100
FORMULA
Recurrence: (8*n-19)*a(n) = (24*n^3 - 41*n^2 - 47*n + 19)*a(n-1) - (n-2)*n*(24*n^3 - 137*n^2 + 240*n - 139)*a(n-2) + (n-3)^2*(n-2)^2*(n-1)*n*(8*n-11)*a(n-3). - Vaclav Kotesovec, Feb 15 2014
a(n) ~ n^(2*n) * exp(n^(1/3) + 3*n^(2/3) - 2*n - 2/3) / sqrt(3) * (1 + 23/(54*n^(1/3)) - 3331/(29160*n^(2/3))). - Vaclav Kotesovec, Feb 15 2014
MATHEMATICA
Table[(n+1)! * n! * HypergeometricPFQ[{n+2, n+1}, {2, 2}, 1]/E, {n, 1, 20}] (* Vaclav Kotesovec, Feb 15 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Oct 12 2003
EXTENSIONS
Corrected typo in a(11) and extended by Vincenzo Librandi, Feb 16 2014
STATUS
approved