This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091033 #9 Nov 03 2022 05:43:48
%S A091033 1,180,25200,4233600,898128000,239740300800,79332244992000,
%T A091033 32011868528640000,15509750302126080000,8898339094906060800000,
%U A091033 5971815866682429603840000,4637851802955964809216000000
%N A091033 Third column (k=4) of array A090438 ((4,2)-Stirling2).
%F A091033 a(n) = A090438(n, 4), n>=2.
%F A091033 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 A091033 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 A091033 From _Amiram Eldar_, Nov 03 2022: (Start)
%F A091033 Sum_{n>=2} 1/a(n) = -20 + 24*Gamma - 16*CoshIntegral(1) + 16*sinh(1) + 8*SinhIntegral(1).
%F A091033 Sum_{n>=2} (-1)^n/a(n) = 4 - 24*gamma + 16*cos(1) + 24*CosIntegral(1) - 16*sin(1) + 8*SinIntegral(1). (End)
%t A091033 a[n_] := (n-1)*(2*n-3)*(2*n)!/4!; Array[a, 12, 2] (* _Amiram Eldar_, Nov 03 2022 *)
%o A091033 (PARI) a(n) = (n-1)*(2*n-3)*(2*n)!/4!; \\ _Amiram Eldar_, Nov 03 2022
%Y A091033 Cf. A091032 (second column of A090438 divided by 8), A091034 (fourth column divided by 24), A000384, A090438.
%Y A091033 Cf. A001620, A049469, A049470, A073742, A099281, A099282, A099283, A099284.
%K A091033 nonn,easy
%O A091033 2,2
%A A091033 _Wolfdieter Lang_, Jan 23 2004