A027798 a(n) = 26*(n+1)*binomial(n+3,13).

286, 4368, 35490, 203840, 928200, 3564288, 11992344, 36279360, 100524060, 258658400, 624660036, 1427794368, 3109779400, 6489974400, 13037895000, 25310900160, 47640468330, 87185170800, 155514818550, 270951408000, 461972150640, 772082488320, 1266697832400

Offset

10,1

Comments

Number of 17-subsequences of [ 1, n ] with just 3 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 10..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.: 26*(11+3x)*x^10/(1-x)^15.

a(n) = C(n+1, 11)*C(n+3, 3). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Mar 16 2016

From Amiram Eldar, Feb 02 2022: (Start)

Sum_{n>=10} 1/a(n) = 11*Pi^2/2 - 631938577/11642400.

Sum_{n>=10} (-1)^n/a(n) = 11*Pi^2/4 + 69632*log(2)/105 - 5667600943/11642400. (End)

Mathematica

Table[26*(n+1)*Binomial[n+3, 13], {n, 10, 30}] (* Harvey P. Dale, Jan 23 2012 *)
Table[Binomial[n + 1, 11] Binomial[n + 3, 3], {n, 10, 32}] (* Michael De Vlieger, Mar 16 2016 *)

Crossrefs

Sequence in context: A204035 A235409 A238251 * A072817 A117994 A221431

Adjacent sequences: A027795 A027796 A027797 * A027799 A027800 A027801

Keyword

nonn

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved