A027807 a(n) = 165*(n+1)*binomial(n+4,11)/4.

330, 4455, 32175, 165165, 675675, 2342340, 7147140, 19691100, 49884120, 117781950, 261891630, 552882330, 1115464350, 2162284740, 4045090500, 7330194300, 12907516050, 22145248125, 37105593525, 60841155375, 97796523825, 154345534200, 239501691000, 365847510600

Offset

7,1

Comments

Number of 16-subsequences of [ 1, n ] with just 4 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 7..1000

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Formula

G.f.: 165*(2+x)*x^7/(1-x)^13.

a(n) = C(n+1, 8)*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>=7} 1/a(n) = 10446643/198450 - 16*Pi^2/3.

Sum_{n>=7} (-1)^(n+1)/a(n) = 8*Pi^2/3 + 8192*log(2)/63 - 23108957/198450. (End)

Mathematica

Table[165 (n + 1) Binomial[n + 4, 11]/4, {n, 7, 30}] (* or *) Table[Binomial[n + 1, 8] Binomial[n + 4, 4], {n, 7, 30}] (* Michael De Vlieger, Mar 16 2016 *)

Crossrefs

Sequence in context: A064262 A126997 A205993 * A104476 A140908 A256586

Adjacent sequences: A027804 A027805 A027806 * A027808 A027809 A027810

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved