A091035 Fifth column (k=6) of array A090438 ((4,2)-Stirling2).

1, 840, 352800, 139708800, 59935075200, 29088489830400, 16183777978368000, 10339833534750720000, 7563588230670151680000, 6303583414831453470720000, 5951909813793488171827200000, 6330667711034891964579840000000

Offset: 3

Author

Wolfdieter Lang, Jan 23 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A091034 (fourth column of A090438 divided by 24), A091036 (sixth column divided by 48), A053134, A090438.

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

Programs

Mathematica

Table[Binomial[2n-2,4] (2n)!/6!,{n,3,20}] (* Harvey P. Dale, Jun 07 2021 *)

PARI

a(n) = binomial(2*n-2, 4)*(2*n)!/6!; \\ Amiram Eldar, Nov 03 2022

Formula

a(n) = A090438(n, 6), n>=3.

a(n) = binomial(2*n-2, 4)*(2*n)!/6! = A053134(n-3)*(2*n)!/6!, n>=3.

E.g.f.: (Sum_{p=2..6} (((-1)^p)*binomial(6, p)*hypergeom([(p-1)/2, p/2], [], 4*x)) - 5)/6! (cf. A090438).

From Amiram Eldar, Nov 03 2022: (Start)

Sum_{n>=3} 1/a(n) = -594 + 1800*Gamma - 1008*cosh(1) - 1800*CoshIntegral(1) + 912*sinh(1) + 1464*SinhIntegral(1).

Sum_{n>=3} (-1)^(n+1)/a(n) = 1554 + 1080*gamma - 1248*cos(1) - 1080*CosIntegral(1) + 240*sin(1) - 1416*SinIntegral(1). (End)