A027771 a(n) = (n+1)*binomial(n+1,11).

11, 144, 1014, 5096, 20475, 69888, 210392, 572832, 1436058, 3359200, 7407036, 15519504, 31097794, 59907456, 111435000, 200880160, 352023165, 601277040, 1003321410, 1638819000, 2624841765, 4128783360, 6386711760, 9727323840, 14602906500, 21628990656

Offset: 10

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

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 Martínez, 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).

Crossrefs

Cf. A000757, A233440.

Programs

Mathematica

Table[(n+1)*Binomial[n+1, 11], {n, 10, 35}] (* Amiram Eldar, Jan 30 2022 *)

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)