A027801 a(n) = 5*(n+1)*binomial(n+4,5)/2.

5, 45, 210, 700, 1890, 4410, 9240, 17820, 32175, 55055, 90090, 141960, 216580, 321300, 465120, 658920, 915705, 1250865, 1682450, 2231460, 2922150, 3782350, 4843800, 6142500, 7719075, 9619155, 11893770, 14599760, 17800200, 21564840, 25970560, 31101840, 37051245

Offset: 1

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 10-subsequences of [ 1, n ] with just 4 contiguous pairs.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A051923.

Programs

Mathematica

Table[5(n+1) Binomial[n+4,5]/2,{n,30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{5,45,210,700,1890,4410,9240},30] (* Harvey P. Dale, Dec 13 2014 *)

Formula

G.f.: 5*(1+2x)*x/(1-x)^7.

a(n) = C(n+1, 2)*C(n+4, 4) - Zerinvary Lajos, May 10 2005, corrected by R. J. Mathar, Feb 13 2016

a(n) = 5*A051923(n-1).

From Amiram Eldar, Jan 28 2022: (Start)

Sum_{n>=1} 1/a(n) = 241/18 - 4*Pi^2/3.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*Pi^2/3 - 64*log(2)/3 + 151/18. (End)