A027792 a(n) = 7*(n+1)*binomial(n+3,7).

35, 336, 1764, 6720, 20790, 55440, 132132, 288288, 585585, 1121120, 2042040, 3564288, 5996172, 9767520, 15465240, 23876160, 36038079, 53300016, 77392700, 110510400, 155405250, 215495280, 294987420, 399016800, 533803725, 706829760, 927034416, 1205033984, 1553364120

Offset

4,1

Comments

Number of 11-subsequences of [ 1, n ] with just 3 contiguous pairs.

Links

Table of n, a(n) for n=4..32.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: 7*(5+3x)*x^4/(1-x)^9.

a(n) = C(n+1, 5)*C(n+3, 3). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Feb 10 2016

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=4} 1/a(n) = 5*Pi^2/2 - 2957/120.

Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/4 + 32*log(2) - 4139/120. (End)

Mathematica

Table[7(n+1)Binomial[n+3, 7], {n, 4, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {35, 336, 1764, 6720, 20790, 55440, 132132, 288288, 585585}, 30] (* Harvey P. Dale, Jan 04 2015 *)

Crossrefs

Sequence in context: A371841 A227058 A372151 * A163935 A101099 A027803

Adjacent sequences: A027789 A027790 A027791 * A027793 A027794 A027795

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved