A027784 a(n) = 11*(n+1)*binomial(n+2,11)/2.

55, 726, 5148, 26026, 105105, 360360, 1089088, 2975544, 7482618, 17551820, 38798760, 81477396, 163601438, 315762216, 588376800, 1062347000, 1864418985, 3188915730, 5327982660, 8713054350, 13970931975, 21998673840, 34062462720, 51926743440, 78021243300

Offset

9,1

Comments

Number of 14-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 9..1000

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Formula

G.f.: 11*(5+x)*x^9/(1-x)^13.

a(n) = C(n+1, 10)*C(n+2, 2). - Zerinvary Lajos, Apr 28 2005; corrected by R. J. Mathar, Mar 15 2016

From Amiram Eldar, Feb 01 2022: (Start)

Sum_{n>=9} 1/a(n) = 5226139/158760 - 10*Pi^2/3.

Sum_{n>=9} (-1)^(n+1)/a(n) = 5*Pi^2/3 + 40960*log(2)/63 - 74154901/158760. (End)

Mathematica

Table[11(n+1) Binomial[n+2, 11]/2, {n, 9, 40}] (* or *) LinearRecurrence[ {13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {55, 726, 5148, 26026, 105105, 360360, 1089088, 2975544, 7482618, 17551820, 38798760, 81477396, 163601438}, 30] (* Harvey P. Dale, May 11 2013 *)

Crossrefs

Sequence in context: A132155 A173377 A053138 * A297523 A221786 A358634

Adjacent sequences: A027781 A027782 A027783 * A027785 A027786 A027787

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved