A027822 a(n) = 42*(n+1)*binomial(n+6,10).

210, 2772, 19404, 96096, 378378, 1261260, 3699696, 9801792, 23891868, 54318264, 116396280, 237025152, 461705244, 864913896, 1565082288, 2745758400, 4684950270, 7795127340, 12676924260, 20190250080, 31547265750, 48432564180, 73156880160, 108851783040

Offset

4,1

Comments

Number of 17-subsequences of [ 1, n ] with just 6 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 4..1000

Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Formula

G.f.: 42*(5+6*x)*x^4/(1-x)^12.

a(n) = C(n+1,5)*C(n+6,6). - Zerinvary Lajos, Jun 08 2005

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=4} 1/a(n) = 5*Pi^2 - 10444891/211680.

Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/2 - 512*log(2)/21 - 1644749/211680. (End)

Mathematica

Table[42*(n + 1)*Binomial[n + 6, 10], {n, 4, 30}] (* Amiram Eldar, Feb 04 2022*)

Crossrefs

Sequence in context: A064260 A027806 A024407 * A024449 A235240 A103604

Adjacent sequences: A027819 A027820 A027821 * A027823 A027824 A027825

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved