A027808 a(n) = 55*(n+1)*binomial(n+4,12).

495, 7150, 55055, 300300, 1301300, 4764760, 15315300, 44341440, 117781950, 290990700, 675745070, 1487285800, 3123300180, 6292363000, 12216990500, 22946695200, 41829913125, 74211187050, 128442439125, 217325608500, 360139579800, 585448578000, 934943638200

Offset

8,1

Comments

Number of 17-subsequences of [ 1, n ] with just 4 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 8..1000

Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Formula

G.f.: 55*(9+4*x)*x^8/(1-x)^14.

a(n) = C(n+1, 9)*C(n+4, 4). - Zerinvary Lajos, May 26 2005

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=8} 1/a(n) = 6*Pi^2 - 631959059/10672200.

Sum_{n>=8} (-1)^n/a(n) = 3*Pi^2 + 77824*log(2)/385 - 1811284381/10672200. (End)

Mathematica

Table[55(n+1)Binomial[n+4, 12], {n, 8, 30}] (* or *) CoefficientList[ Series[(55(4x+9))/(x-1)^14, {x, 0, 22}], x] (* Harvey P. Dale, Nov 20 2011 *)

Crossrefs

Sequence in context: A099009 A055160 A055157 * A104478 A133352 A140913

Adjacent sequences: A027805 A027806 A027807 * A027809 A027810 A027811

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved