OFFSET
12,1
COMMENTS
Number of 15-subsequences of [ 1, n ] with just 1 contiguous pair.
LINKS
T. D. Noe, Table of n, a(n) for n = 12..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 (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
FORMULA
G.f.: (13+x)*x^12/(1-x)^15.
From Amiram Eldar, Jan 30 2022: (Start)
Sum_{n>=12} 1/a(n) = 13*Pi^2/6 - 8183956651/384199200.
Sum_{n>=12} (-1)^n/a(n) = 13*Pi^2/12 + 34451456*log(2)/3465 - 2651886676309/384199200. (End)
MATHEMATICA
(#+1)Binomial[#+1, 13]&/@Range[12, 40] (* Harvey P. Dale, Mar 18 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved