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

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

Offset

3,2

Links

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

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)

Mathematica

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

Prog

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

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.

Sequence in context: A022052 A055353 A107516 * A181203 A091036 A091038

Adjacent sequences: A091032 A091033 A091034 * A091036 A091037 A091038

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 23 2004

Status

approved