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%I #9 Nov 03 2022 05:43:48
%S 1,180,25200,4233600,898128000,239740300800,79332244992000,
%T 32011868528640000,15509750302126080000,8898339094906060800000,
%U 5971815866682429603840000,4637851802955964809216000000
%N Third column (k=4) of array A090438 ((4,2)-Stirling2).
%F a(n) = A090438(n, 4), n>=2.
%F a(n) = (n-1)*(2*n-3)*(2*n)!/4! = binomial(2*(n-1), 2)*(2*n)!/4! = A000384(n-1)*(2*n)!/4!, n>=2.
%F E.g.f.: (6*hypergeom([1/2, 1], [], 4*x) - 4*hypergeom([1, 3/2], [], 4*x) + hypergeom([3/2, 2], [], 4*x) -3)/4! (cf. A090438).
%F From _Amiram Eldar_, Nov 03 2022: (Start)
%F Sum_{n>=2} 1/a(n) = -20 + 24*Gamma - 16*CoshIntegral(1) + 16*sinh(1) + 8*SinhIntegral(1).
%F Sum_{n>=2} (-1)^n/a(n) = 4 - 24*gamma + 16*cos(1) + 24*CosIntegral(1) - 16*sin(1) + 8*SinIntegral(1). (End)
%t a[n_] := (n-1)*(2*n-3)*(2*n)!/4!; Array[a, 12, 2] (* _Amiram Eldar_, Nov 03 2022 *)
%o (PARI) a(n) = (n-1)*(2*n-3)*(2*n)!/4!; \\ _Amiram Eldar_, Nov 03 2022
%Y Cf. A091032 (second column of A090438 divided by 8), A091034 (fourth column divided by 24), A000384, A090438.
%Y Cf. A001620, A049469, A049470, A073742, A099281, A099282, A099283, A099284.
%K nonn,easy
%O 2,2
%A _Wolfdieter Lang_, Jan 23 2004
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