OFFSET
0,2
FORMULA
a(n) is the n-th power moment of a positive function on a positive half-axis: a(n)=int(x^n*2*hypergeom([], [1, 2], x)*x^(1/2)*BesselK(1, 2*sqrt(x))/exp(1), x=0..infinity), n=0, 1...
Recurrence: (8*n^2 - 19*n + 9)*a(n) = (24*n^4 - 25*n^3 - 50*n^2 + 36*n + 1)*a(n-1) - (n-1)^2*(24*n^4 - 105*n^3 + 119*n^2 - 10*n - 24)*a(n-2) + (n-3)*(n-2)^2*(n-1)^3*(8*n^2 - 3*n - 2)*a(n-3). - Vaclav Kotesovec, Jul 05 2018
MATHEMATICA
Table[HypergeometricPFQ[{n+1, n+2}, {1, 2}, 1] *n! *(n+1)! /E, {n, 0, 20}] (* Vaclav Kotesovec, Jul 05 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Apr 22 2002
STATUS
approved