A091033 Third column (k=4) of array A090438 ((4,2)-Stirling2).

1, 180, 25200, 4233600, 898128000, 239740300800, 79332244992000, 32011868528640000, 15509750302126080000, 8898339094906060800000, 5971815866682429603840000, 4637851802955964809216000000

Offset

2,2

Links

Table of n, a(n) for n=2..13.

Formula

a(n) = A090438(n, 4), n>=2.

a(n) = (n-1)*(2*n-3)*(2*n)!/4! = binomial(2*(n-1), 2)*(2*n)!/4! = A000384(n-1)*(2*n)!/4!, n>=2.

E.g.f.: (6*hypergeom([1/2, 1], [], 4*x) - 4*hypergeom([1, 3/2], [], 4*x) + hypergeom([3/2, 2], [], 4*x) -3)/4! (cf. A090438).

From Amiram Eldar, Nov 03 2022: (Start)

Sum_{n>=2} 1/a(n) = -20 + 24*Gamma - 16*CoshIntegral(1) + 16*sinh(1) + 8*SinhIntegral(1).

Sum_{n>=2} (-1)^n/a(n) = 4 - 24*gamma + 16*cos(1) + 24*CosIntegral(1) - 16*sin(1) + 8*SinIntegral(1). (End)

Mathematica

a[n_] := (n-1)*(2*n-3)*(2*n)!/4!; Array[a, 12, 2] (* Amiram Eldar, Nov 03 2022 *)

Prog

(PARI) a(n) = (n-1)*(2*n-3)*(2*n)!/4!; \\ Amiram Eldar, Nov 03 2022

Crossrefs

Cf. A091032 (second column of A090438 divided by 8), A091034 (fourth column divided by 24), A000384, A090438.

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

Sequence in context: A217791 A035830 A244056 * A146530 A057867 A075871

Adjacent sequences: A091030 A091031 A091032 * A091034 A091035 A091036

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 23 2004

Status

approved