OFFSET
10,1
COMMENTS
Number of 13-subsequences of [ 1, n ] with just 1 contiguous pair.
1214673*a(n) is the number of permutations of (n+1) symbols that 11-commute with an (n+1)-cycle (see A233440 for definition), where 1214673 = A000757(11). - Luis Manuel Rivera MartÃnez, Feb 07 2014
LINKS
T. D. Noe, Table of n, a(n) for n = 10..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 (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
G.f.: (11+x)*x^10/(1-x)^13.
From Amiram Eldar, Jan 30 2022: (Start)
Sum_{n>=10} 1/a(n) = 11*Pi^2/6 - 57138257/3175200.
Sum_{n>=10} (-1)^n/a(n) = 11*Pi^2/12 + 822272*log(2)/315 - 5773608863/3175200. (End)
MATHEMATICA
Table[(n+1)*Binomial[n+1, 11], {n, 10, 35}] (* Amiram Eldar, Jan 30 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved