A027773 a(n) = (n+1)*binomial(n+1,13).

13, 196, 1575, 8960, 40460, 154224, 515508, 1550400, 4273290, 10943240, 26313518, 59907456, 130007500, 270415600, 541574100, 1048380480, 1968053535, 3592795500, 6393845325, 11115955200, 18914492520, 31551447840, 51671823000, 83188425600, 131811290100

Offset: 12

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

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).

Programs

Mathematica

(#+1)Binomial[#+1,13]&/@Range[12,40]  (* Harvey P. Dale, Mar 18 2011 *)

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)