A027787 a(n) = 7*(n+1)*binomial(n+2,14).

91, 1470, 12600, 76160, 364140, 1465128, 5155080, 16279200, 47006190, 125847260, 315762216, 748843200, 1690097500, 3650610600, 7582037400, 15201516960, 29520803025, 55688330250, 102301525200, 183413260800, 321546372840, 552150337200, 930092814000

Offset

12,1

Comments

Number of 17-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 12..1000

Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Formula

G.f.: 7*(13+2x)*x^12/(1-x)^16.

a(n) = C(n+1, 13)*C(n+2, 2). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Mar 16 2016

From Amiram Eldar, Feb 01 2022: (Start)

Sum_{n>=12} 1/a(n) = 13*Pi^2/3 - 106775635663/2497294800.

Sum_{n>=12} (-1)^n/a(n) = 13*Pi^2/6 + 12132352*log(2)/3465 - 6114275457217/2497294800. (End)

Mathematica

Table[7(n+1)Binomial[n+2, 14], {n, 12, 40}] (* Harvey P. Dale, Jul 18 2011 *)

Crossrefs

Sequence in context: A195221 A213559 A120756 * A333112 A140667 A221939

Adjacent sequences: A027784 A027785 A027786 * A027788 A027789 A027790

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Extensions

Offset corrected by Harvey P. Dale, Jul 18 2011

Status

approved