A027820 a(n) = 28*(n+1)*binomial(n+6,8)/3.

28, 336, 2100, 9240, 32340, 96096, 252252, 600600, 1321320, 2722720, 5309304, 9876048, 17635800, 30387840, 50736840, 82372752, 130423524, 201894000, 306205900, 455855400, 667206540, 961440480, 1365682500, 1914330600, 2650611600, 3628392768, 4914279216, 6590029600

Offset

2,1

Comments

Number of 15-subsequences of [ 1, n ] with just 6 contiguous pairs.

Links

Table of n, a(n) for n=2..29.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: 28*(1+2x)*x^2/(1-x)^10.

a(n) = C(n+1, 3)*C(n+6, 6). - Zerinvary Lajos, Jun 08 2005; corrected by R. J. Mathar, Feb 10 2016

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=2} 1/a(n) = 3*Pi^2 - 289781/9800.

Sum_{n>=2} (-1)^n/a(n) = 3*Pi^2/2 - 2112*log(2)/35 + 265141/9800. (End)

Mathematica

Table[28(n+1) Binomial[n+6, 8]/3, {n, 2, 30}] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {28, 336, 2100, 9240, 32340, 96096, 252252, 600600, 1321320, 2722720}, 30] (* Harvey P. Dale, Sep 12 2017 *)

Prog

(PARI) a(n)=28*(n+1)*binomial(n+6, 8)/3 \\ Charles R Greathouse IV, May 22 2013

Crossrefs

Sequence in context: A241038 A055753 A159520 * A092713 A134288 A200968

Adjacent sequences: A027817 A027818 A027819 * A027821 A027822 A027823

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved