A027795 a(n) = 15*(n+1)*binomial(n+3,10).

120, 1485, 9900, 47190, 180180, 585585, 1681680, 4375800, 10501920, 23556390, 49884120, 100524060, 193993800, 360380790, 647214480, 1127722200, 1912224600, 3163606875, 5118012900, 8112154050, 12618906300, 19293191775, 29030508000, 43040883600, 62941507200

Offset

7,1

Comments

Number of 14-subsequences of [ 1, n ] with just 3 contiguous pairs.

Links

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

Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Formula

G.f.: 15*(8+3x)*x^7/(1-x)^12.

a(n) = C(n+1, 8)*C(n+3, 3). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Mar 16 2016

From Amiram Eldar, Feb 01 2022: (Start)

Sum_{n>=7} 1/a(n) = 10448407/264600 - 4*Pi^2.

Sum_{n>=7} (-1)^(n+1)/a(n) = 2*Pi^2 + 17408*log(2)/105 - 35628037/264600. (End)

Mathematica

Table[15 (n + 1) Binomial[n + 3, 10], {n, 7, 31}] (* or *) Table[Binomial[n + 1, 8] Binomial[n + 3, 3], {n, 7, 31}] (* Michael De Vlieger, Mar 16 2016 *)

Crossrefs

Sequence in context: A175112 A257996 A183597 * A223427 A282899 A340580

Adjacent sequences: A027792 A027793 A027794 * A027796 A027797 A027798

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved