A027774 a(n) = (n+1)*binomial(n+1,14).

14, 225, 1920, 11560, 55080, 220932, 775200, 2441880, 7034940, 18795370, 47070144, 111435000, 251100200, 541574100, 1123264800, 2249204040, 4362680250, 8220658275, 15085939200, 27020703600, 47327171760, 81198579000, 136666699200, 225962211600, 367443055800

Offset: 13

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 16-subsequences of [ 1, n ] with just 1 contiguous pair.

Links

• T. D. Noe, Table of n, a(n) for n = 13..1000
• 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 (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Programs

Mathematica

Table[(n+1)Binomial[n+1,14],{n,13,40}] (* Harvey P. Dale, Nov 04 2017 *)

Formula

G.f.: (14+x)*x^13/(1-x)^16.

From Amiram Eldar, Jan 30 2022: (Start)

Sum_{n>=13} 1/a(n) = 107159834863/4637833200 - 7*Pi^2/3.

Sum_{n>=13} (-1)^(n+1)/a(n) = 7*Pi^2/6 + 125673472*log(2)/6435 - 62835162326017/4637833200. (End)