A091032 Second column (k=3) of array A090438 ((4,2)-Stirling2) divided by 8.

1, 60, 5040, 604800, 99792000, 21794572800, 6102480384000, 2134124568576000, 912338253066240000, 468333636574003200000, 284372184127734743040000, 201645730563302817792000000, 165147853331345007771648000000

Offset

2,2

Links

Table of n, a(n) for n=2..14.

Formula

a(n) = A090438(n, 3)/8 = (n-1)*(2*n)!/4!

E.g.f.: (-3*hypergeom([1/2, 1], [], 4*x) + hypergeom([1, 3/2], [], 4*x) + 2)/(8*3!) (cf. A090438).

From Amiram Eldar, Nov 03 2022: (Start)

Sum_{n>=2} 1/a(n) = 60 - 24*Gamma - 24*cosh(1) + 24*CoshIntegral(1) - 24*sinh(1).

Sum_{n>=2} (-1)^n/a(n) = -12 + 24*gamma - 24*cos(1) - 24*CosIntegral(1) + 24*SinIntegral(1). (End)

Mathematica

a[n_] := (n - 1)*(2*n)!/4!; Array[a, 13, 2] (* Amiram Eldar, Nov 03 2022 *)

Prog

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

Crossrefs

Cf. A002674 (first column of A090438), A091033 (third column), A090438.

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

Sequence in context: A074076 A084274 A289307 * A328951 A178785 A091753

Adjacent sequences: A091029 A091030 A091031 * A091033 A091034 A091035

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 23 2004

Status

approved