OFFSET
13,1
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).
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)
MATHEMATICA
Table[(n+1)Binomial[n+1, 14], {n, 13, 40}] (* Harvey P. Dale, Nov 04 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved