A027786 a(n) = 13*(n+1)*binomial(n+2,13)/2.

78, 1183, 9555, 54600, 247520, 946764, 3174444, 9573720, 26453700, 67897830, 163601438, 373173528, 811246800, 1690097500, 3389852700, 6571099080, 12351232530, 22574731725, 40219349625, 69995780400, 119218619520, 199052516520, 326270653800, 525704634000

Offset

11,1

Comments

Number of 16-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 11..1000

Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Formula

G.f.: 13*(6+x)*x^11/(1-x)^15.

a(n) = C(n+1, 12)*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>=11} 1/a(n) = 632203177/16008300 - 4*Pi^2.

Sum_{n>=11} (-1)^(n+1)/a(n) = 2*Pi^2 + 2277376*log(2)/1155 - 22194594643/16008300. (End)

Mathematica

Table[13 (n + 1) Binomial[n + 2, 13]/2, {n, 11, 40}] (* Wesley Ivan Hurt, Mar 30 2017 *)

Crossrefs

Sequence in context: A128951 A370209 A272383 * A175383 A190396 A230521

Adjacent sequences: A027783 A027784 A027785 * A027787 A027788 A027789

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved