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%I #8 Jul 05 2018 12:20:15
%S 1,7,141,5305,313333,26405391,2986704817,434460962041,78746410575945,
%T 17355333316259863,4561636814725190101,1407386778722787214617,
%U 503024214435970044854461
%N a(n)= 2F2(n+1, n+2; 1, 2; 1) *n! *(n+1)! /exp(1), where 2F2 is the generalized hypergeometric function.
%F 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...
%F 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
%t Table[HypergeometricPFQ[{n+1, n+2},{1, 2},1] *n! *(n+1)! /E, {n,0,20}] (* _Vaclav Kotesovec_, Jul 05 2018 *)
%K nonn
%O 0,2
%A _Karol A. Penson_, Apr 22 2002
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