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 A091032 #12 Apr 19 2025 06:14:21
%S A091032 1,60,5040,604800,99792000,21794572800,6102480384000,2134124568576000,
%T A091032 912338253066240000,468333636574003200000,284372184127734743040000,
%U A091032 201645730563302817792000000,165147853331345007771648000000
%N A091032 Second column (k=3) of array A090438 ((4,2)-Stirling2) divided by 8.
%H A091032 John Campbell, <a href="https://doi.org/10.5206/mt.v5i1.16724">Applications of Gosper’s nonlocal derangement identity</a>, Maple Transactions, 5, 1, Article 16724, Feb. 2025.
%F A091032 a(n) = A090438(n, 3)/8 = (n-1)*(2*n)!/4!
%F A091032 E.g.f.: (-3*hypergeom([1/2, 1], [], 4*x) + hypergeom([1, 3/2], [], 4*x) + 2)/(8*3!) (cf. A090438).
%F A091032 From _Amiram Eldar_, Nov 03 2022: (Start)
%F A091032 Sum_{n>=2} 1/a(n) = 60 - 24*Gamma - 24*cosh(1) + 24*CoshIntegral(1) - 24*sinh(1).
%F A091032 Sum_{n>=2} (-1)^n/a(n) = -12 + 24*gamma - 24*cos(1) - 24*CosIntegral(1) + 24*SinIntegral(1). (End)
%F A091032 a(n+1) = Sum_{j = 1..n} (-1)^(n+j) * j^(2*n+2) * binomial(2*n, n-j) (Campbell, Eq. 17). - _Peter Bala_, Mar 30 2025
%t A091032 a[n_] := (n - 1)*(2*n)!/4!; Array[a, 13, 2] (* _Amiram Eldar_, Nov 03 2022 *)
%o A091032 (PARI) a(n) = (n-1)*(2*n)!/4!; \\ _Amiram Eldar_, Nov 03 2022
%Y A091032 Cf. A002674 (first column of A090438), A091033 (third column), A090438.
%Y A091032 Cf. A001620, A049470, A073742, A073743, A099281, A099282, A099284.
%K A091032 nonn,easy
%O A091032 2,2
%A A091032 _Wolfdieter Lang_, Jan 23 2004