A027776 a(n) = (n+1)*binomial(n+1,16).

16, 289, 2754, 18411, 96900, 427329, 1641486, 5638611, 17651304, 51074375, 138105110, 352023165, 851809140, 1968053535, 4362680250, 9316746045, 19234572480, 38504502630, 74934688620, 142097513250, 263083395960, 476403662790, 845119028340, 1470739178610

Offset: 15

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 18-subsequences of [ 1, n ] with just 1 contiguous pair.

Links

• T. D. Noe, Table of n, a(n) for n = 15..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 (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).

Programs

Mathematica

Table[(n + 1) Binomial[n + 1, 16], {n, 15, 100}] (* T. D. Noe, Mar 28 2012 *)

Formula

G.f.: (16+x)*x^15/(1-x)^18.

From Amiram Eldar, Jan 30 2022: (Start)

Sum_{n>=15} 1/a(n) = 107074439839/4058104050 - 8*Pi^2/3.

Sum_{n>=15} (-1)^(n+1)/a(n) = 4*Pi^2/3 + 684654592*log(2)/9009 - 30545942365399/579729150. (End)

Extensions

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