A027768 a(n) = (n+1)*binomial(n+1,8).

8, 81, 450, 1815, 5940, 16731, 42042, 96525, 205920, 413270, 787644, 1436058, 2519400, 4273290, 7034940, 11277222, 17651304, 27039375, 40619150, 59942025, 87026940, 124472205, 175587750, 244550475, 336585600, 458177148, 617310936, 823753700, 1089372240

Offset: 7

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 10-subsequences of [ 1, n ] with just 1 contiguous pair.

1625*a(n) is the number of permutations of (n+1) symbols that 8-commute with an (n+1)-cycle (see A233440 for definition), where 1625 = A000757(8). - Luis Manuel Rivera Martínez, Feb 07 2014

Links

• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A000757, A233440.

Programs

Mathematica

Table[(n+1)Binomial[n+1,8],{n,7,40}] (* Harvey P. Dale, Jul 08 2017 *)

PARI

a(n) = (n+1)*binomial(n+1, 8); \\ Michel Marcus, Jan 31 2014

Formula

G.f.: (8+x)*x^7/(1-x)^10.

From Amiram Eldar, Jan 30 2022: (Start)

Sum_{n>=7} 1/a(n) = 48877/3675 - 4*Pi^2/3.

Sum_{n>=7} (-1)^(n+1)/a(n) = 2*Pi^2/3 + 38656*log(2)/105 - 2884681/11025. (End)

Extensions

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