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%I #9 Nov 03 2022 05:43:41
%S 1,280,70560,19958400,6659452800,2644408166400,1244905998336000,
%T 689322235650048000,444916954745303040000,331767548149023866880000,
%U 283424276847308960563200000,275246422218908346286080000000
%N Fourth column (k=5) of array A090438 ((4,2)-Stirling2) divided by 24.
%F a(n) = A090438(n, 5)/24, n>=3.
%F a(n) = (n-1)*(n-2)*(2*n-3)*(2*n)!/(5!*(3!)^2), n>=3.
%F E.g.f.: (Sum_{p=2..5} (((-1)^(p+1))*binomial(5, p)*hypergeom([(p-1)/2, p/2], [], 4*x)) + 4)/(5!*4!) (cf. A090438).
%F From _Amiram Eldar_, Nov 03 2022: (Start)
%F Sum_{n>=3} 1/a(n) = 2010 - 4680*Gamma + 1800*cosh(1) + 4680*CoshIntegral(1) - 2520*sinh(1) - 2880*SinhIntegral(1).
%F Sum_{n>=3} (-1)^(n+1)/a(n) = -2010 - 3960*gamma + 3240*cos(1) + 3960*CosIntegral(1) - 1800*sin(1) + 2880*SinIntegral(1). (End)
%t a[n_] := (n - 1)*(n - 2)*(2*n - 3)*(2*n)!/(5!*(3!)^2); Array[a, 12, 3] (* _Amiram Eldar_, Nov 03 2022 *)
%o (PARI) a(n) = (n-1)*(n-2)*(2*n-3)*(2*n)!/(5!*(3!)^2); \\ _Amiram Eldar_, Nov 03 2022
%Y Cf. A091033 (third column of A090438), A091035 (fifth column), 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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