A027767 a(n) = (n+1)*binomial(n+1,7).

7, 64, 324, 1200, 3630, 9504, 22308, 48048, 96525, 183040, 330616, 572832, 957372, 1550400, 2441880, 3751968, 5638611, 8306496, 12017500, 17102800, 23976810, 33153120, 45262620, 61074000, 81516825, 107707392, 140977584, 182906944, 235358200, 300516480, 380932464

Offset

6,1

Comments

Number of 9-subsequences of [ 1, n ] with just 1 contiguous pair.

229*a(n) is the number of permutations of (n+1) symbols that 7-commute with an (n+1)-cycle (see A233440 for definition), where 229 = A000757(7). - Luis Manuel Rivera Martínez, Feb 07 2014

Links

Table of n, a(n) for n=6..36.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: (7+x)*x^6/(1-x)^9.

From Amiram Eldar, Jan 30 2022: (Start)

Sum_{n>=6} 1/a(n) = 7*Pi^2/6 - 6811/600.

Sum_{n>=6} (-1)^n/a(n) = 7*Pi^2/12 + 2912*log(2)/15 - 252343/1800. (End)

Mathematica

Table[(n+1)Binomial[n+1, 7], {n, 6, 40}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {7, 64, 324, 1200, 3630, 9504, 22308, 48048, 96525}, 30] (* Harvey P. Dale, Mar 13 2016 *)

Crossrefs

Cf. A000757, A233440.

Sequence in context: A116231 A195630 A136955 * A055537 A333991 A159617

Adjacent sequences: A027764 A027765 A027766 * A027768 A027769 A027770

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Extensions

Incorrect formula deleted by R. J. Mathar, Feb 13 2016

Status

approved