A027809 a(n) = 143*(n+1)*binomial(n+4,13)/2.

715, 11011, 90090, 520520, 2382380, 9189180, 31039008, 94225560, 261891630, 675745070, 1636014380, 3747960216, 8180071900, 17103786700, 34420042800, 66927861000, 126159017985, 231196390425, 412918656150, 720279159600, 1229442013800, 2056876004040

Offset

9,1

Comments

Number of 18-subsequences of [ 1, n ] with just 4 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 9..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.: 143*(5+2x)*x^9/(1-x)^15.

a(n) = C(n+1, 10)*C(n+4, 4). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Mar 16 2016

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=9} 1/a(n) = 631996789/9604980 - 20*Pi^2/3.

Sum_{n>=9} (-1)^(n+1)/a(n) = 10*Pi^2/3 + 212992*log(2)/693 - 2362196911/9604980. (End)

Mathematica

Table[143 (n + 1) Binomial[n + 4, 13]/2, {n, 9, 30}] (* or *) Table[Binomial[n + 1, 10] Binomial[n + 4, 4], {n, 9, 30}] (* Michael De Vlieger, Mar 16 2016 *)

Crossrefs

Sequence in context: A255788 A029565 A154042 * A222912 A266107 A030537

Adjacent sequences: A027806 A027807 A027808 * A027810 A027811 A027812

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved