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%I #11 Nov 03 2022 05:43:33
%S 1,840,352800,139708800,59935075200,29088489830400,16183777978368000,
%T 10339833534750720000,7563588230670151680000,
%U 6303583414831453470720000,5951909813793488171827200000,6330667711034891964579840000000
%N Fifth column (k=6) of array A090438 ((4,2)-Stirling2).
%F a(n) = A090438(n, 6), n>=3.
%F a(n) = binomial(2*n-2, 4)*(2*n)!/6! = A053134(n-3)*(2*n)!/6!, n>=3.
%F E.g.f.: (Sum_{p=2..6} (((-1)^p)*binomial(6, p)*hypergeom([(p-1)/2, p/2], [], 4*x)) - 5)/6! (cf. A090438).
%F From _Amiram Eldar_, Nov 03 2022: (Start)
%F Sum_{n>=3} 1/a(n) = -594 + 1800*Gamma - 1008*cosh(1) - 1800*CoshIntegral(1) + 912*sinh(1) + 1464*SinhIntegral(1).
%F Sum_{n>=3} (-1)^(n+1)/a(n) = 1554 + 1080*gamma - 1248*cos(1) - 1080*CosIntegral(1) + 240*sin(1) - 1416*SinIntegral(1). (End)
%t Table[Binomial[2n-2,4] (2n)!/6!,{n,3,20}] (* _Harvey P. Dale_, Jun 07 2021 *)
%o (PARI) a(n) = binomial(2*n-2, 4)*(2*n)!/6!; \\ _Amiram Eldar_, Nov 03 2022
%Y Cf. A091034 (fourth column of A090438 divided by 24), A091036 (sixth column divided by 48), A053134, A090438.
%Y Cf. A001620, A049469, A049470, A073742, A073743, A099281, A099282, A099283, A099284.
%K nonn,easy
%O 3,2
%A _Wolfdieter Lang_, Jan 23 2004
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