A091034 Fourth column (k=5) of array A090438 ((4,2)-Stirling2) divided by 24.

1, 280, 70560, 19958400, 6659452800, 2644408166400, 1244905998336000, 689322235650048000, 444916954745303040000, 331767548149023866880000, 283424276847308960563200000, 275246422218908346286080000000

Offset

3,2

Links

Table of n, a(n) for n=3..14.

Formula

a(n) = A090438(n, 5)/24, n>=3.

a(n) = (n-1)*(n-2)*(2*n-3)*(2*n)!/(5!*(3!)^2), n>=3.

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).

From Amiram Eldar, Nov 03 2022: (Start)

Sum_{n>=3} 1/a(n) = 2010 - 4680*Gamma + 1800*cosh(1) + 4680*CoshIntegral(1) - 2520*sinh(1) - 2880*SinhIntegral(1).

Sum_{n>=3} (-1)^(n+1)/a(n) = -2010 - 3960*gamma + 3240*cos(1) + 3960*CosIntegral(1) - 1800*sin(1) + 2880*SinIntegral(1). (End)

Mathematica

a[n_] := (n - 1)*(n - 2)*(2*n - 3)*(2*n)!/(5!*(3!)^2); Array[a, 12, 3] (* Amiram Eldar, Nov 03 2022 *)

Prog

(PARI) a(n) = (n-1)*(n-2)*(2*n-3)*(2*n)!/(5!*(3!)^2); \\ Amiram Eldar, Nov 03 2022

Crossrefs

Cf. A091033 (third column of A090438), A091035 (fifth column), A090438.

Cf. A001620, A049469, A049470, A073742, A073743, A099281, A099282, A099283, A099284.

Sequence in context: A272715 A282439 A255498 * A294165 A259079 A296506

Adjacent sequences: A091031 A091032 A091033 * A091035 A091036 A091037

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 23 2004

Status

approved