A027793 a(n) = 28*(n+1)*binomial(n+3,8)/3.

56, 588, 3360, 13860, 46200, 132132, 336336, 780780, 1681680, 3403400, 6534528, 11992344, 21162960, 36085560, 59690400, 96101544, 151016712, 232178100, 349949600, 518017500, 754233480, 1081620540, 1529564400, 2135214900, 2945124000, 4017149136, 5422652928

Offset

5,1

Comments

Number of 12-subsequences of [ 1, n ] with just 3 contiguous pairs.

Links

Table of n, a(n) for n=5..31.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: 28*(2+x)*x^5/(1-x)^10.

a(n) = C(n+1, 6)*C(n+3, 3). - Zerinvary Lajos, May 13 2005; corrected by R. J. Mathar, Feb 10 2016

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=5} 1/a(n) = 145181/4900 - 3*Pi^2.

Sum_{n>=5} (-1)^(n+1)/a(n) = 3*Pi^2/2 + 2112*log(2)/35 - 277411/4900. (End)

Mathematica

Table[28(n+1) Binomial[n+3, 8]/3, {n, 5, 30}] (* Harvey P. Dale, Oct 24 2020 *)

Crossrefs

Sequence in context: A219712 A244429 A005931 * A244945 A055747 A234106

Adjacent sequences: A027790 A027791 A027792 * A027794 A027795 A027796

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved