%I #8 Nov 03 2022 05:43:52
%S 1,60,5040,604800,99792000,21794572800,6102480384000,2134124568576000,
%T 912338253066240000,468333636574003200000,284372184127734743040000,
%U 201645730563302817792000000,165147853331345007771648000000
%N Second column (k=3) of array A090438 ((4,2)-Stirling2) divided by 8.
%F a(n) = A090438(n, 3)/8 = (n-1)*(2*n)!/4!
%F E.g.f.: (-3*hypergeom([1/2, 1], [], 4*x) + hypergeom([1, 3/2], [], 4*x) + 2)/(8*3!) (cf. A090438).
%F From _Amiram Eldar_, Nov 03 2022: (Start)
%F Sum_{n>=2} 1/a(n) = 60 - 24*Gamma - 24*cosh(1) + 24*CoshIntegral(1) - 24*sinh(1).
%F Sum_{n>=2} (-1)^n/a(n) = -12 + 24*gamma - 24*cos(1) - 24*CosIntegral(1) + 24*SinIntegral(1). (End)
%t a[n_] := (n - 1)*(2*n)!/4!; Array[a, 13, 2] (* _Amiram Eldar_, Nov 03 2022 *)
%o (PARI) a(n) = (n-1)*(2*n)!/4!; \\ _Amiram Eldar_, Nov 03 2022
%Y Cf. A002674 (first column of A090438), A091033 (third column), A090438.
%Y Cf. A001620, A049470, A073742, A073743, A099281, A099282, A099284.
%K nonn,easy
%O 2,2
%A _Wolfdieter Lang_, Jan 23 2004