A027772 a(n) = (n+1)*binomial(n+1,12).

12, 169, 1274, 6825, 29120, 105196, 334152, 957372, 2519400, 6172530, 14226212, 31097794, 64899744, 130007500, 251100200, 469364220, 851809140, 1504982115, 2594796750, 4374736275, 7225370880, 11708971560, 18644037360, 29205813000, 45060397200, 68541870852

Offset: 11

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 14-subsequences of [ 1, n ] with just 1 contiguous pair.

Links

• T. D. Noe, Table of n, a(n) for n = 11..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 (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Programs

Mathematica

Table[(n+1)Binomial[n+1,12],{n,11,40}] (* or *) LinearRecurrence[{14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1},{12,169,1274,6825,29120,105196,334152,957372,2519400,6172530,14226212,31097794,64899744,130007500},30] (* Harvey P. Dale, Mar 13 2018 *)

Formula

G.f.: (12+x)*x^11/(1-x)^14.

From Amiram Eldar, Jan 30 2022: (Start)

Sum_{n>=11} 1/a(n) = 634871227/32016600 - 2*Pi^2.

Sum_{n>=11} (-1)^(n+1)/a(n) = Pi^2 + 5869568*log(2)/1155 - 113091604693/32016600. (End)