A070074 a(n)= 2F2(n+1, n+2; 1, 2; 1) *n! *(n+1)! /exp(1), where 2F2 is the generalized hypergeometric function.

1, 7, 141, 5305, 313333, 26405391, 2986704817, 434460962041, 78746410575945, 17355333316259863, 4561636814725190101, 1407386778722787214617, 503024214435970044854461

Offset

0,2

Links

Table of n, a(n) for n=0..12.

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

Sequence in context: A191956 A215042 A221267 * A051397 A322064 A179569

Adjacent sequences: A070071 A070072 A070073 * A070075 A070076 A070077

Keyword

nonn

Author

Karol A. Penson, Apr 22 2002

Status

approved