A027811 a(n) = 3*(n+1)*binomial(n+5,6).

6, 63, 336, 1260, 3780, 9702, 22176, 46332, 90090, 165165, 288288, 482664, 779688, 1220940, 1860480, 2767464, 4029102, 5753979, 8075760, 11157300, 15195180, 20424690, 27125280, 35626500, 46314450, 59638761, 76120128

Offset

1,1

Comments

Number of 12-subsequences of [ 1, n ] with just 5 contiguous pairs.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: 3*(2+5x)*x/(1-x)^8.

a(n) = C(n+1, 2)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=1} 1/a(n) = 5989/360 - 5*Pi^2/3.

Sum_{n>=1} (-1)^(n+1)/a(n) = 5*Pi^2/6 - 128*log(2)/3 + 7741/360. (End)

Mathematica

Table[3(n+1)Binomial[n+5, 6], {n, 30}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {6, 63, 336, 1260, 3780, 9702, 22176, 46332}, 30] (* or *) CoefficientList[Series[(3(2+5x))/(x-1)^8, {x, 0, 30}], x] (* Harvey P. Dale, Nov 28 2021 *)

Crossrefs

Sequence in context: A158987 A339239 A055005 * A027950 A184447 A053700

Adjacent sequences: A027808 A027809 A027810 * A027812 A027813 A027814

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved