A027819 a(n) = 7*(n+1)*binomial(n+6,7)/2.

7, 84, 504, 2100, 6930, 19404, 48048, 108108, 225225, 440440, 816816, 1447992, 2469012, 4069800, 6511680, 10147368, 15444891, 23015916, 33649000, 48348300, 68378310, 95315220, 131105520, 178132500, 239291325, 318073392, 418660704, 546031024, 706074600, 905723280

Offset: 1

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 14-subsequences of [ 1, n ] with just 6 contiguous pairs.

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A052181.

Programs

Mathematica

Table[7*(n + 1)*Binomial[n + 6, 7]/2, {n, 1, 50}] (* Amiram Eldar, Feb 03 2022 *)

Formula

a(n) = 7*A052181(n).

G.f.: 7*(1+3*x)*x/(1-x)^9.

a(n) = C(n+1,2)*C(n+6,6). - Zerinvary Lajos, May 26 2005

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=1} 1/a(n) = 5969/300 - 2*Pi^2.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2 - 384*log(2)/5 + 13049/300. (End)