A027788 a(n) = 15*(n+1)*binomial(n+2,15)/2.

105, 1800, 16320, 104040, 523260, 2209320, 8139600, 26860680, 80901810, 225544440, 588376800, 1448655000, 3389852700, 7582037400, 16287339600, 33738060600, 67621543875, 131530532400, 248917996800, 459351961200, 828225505800, 1461574422000, 2528333935200

Offset

13,1

Comments

Number of 18-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 13..1000

Index entries for linear recurrences with constant coefficients, signature (17,-136,680, -2380, 6188,-12376,19448,-24310,24310,-19448,12376, -6188,2380,-680,136, -17,1).

Formula

G.f.: 15*(7+x)*x^13/(1-x)^17.

a(n) = C(n+1, 14)*C(n+2, 2). - Zerinvary Lajos, Apr 28 2005; corrected by R. J. Mathar, Mar 16 2016

From Amiram Eldar, Feb 01 2022: (Start)

Sum_{n>=13} 1/a(n) = 15261223009/331273800 - 14*Pi^2/3.

Sum_{n>=13} (-1)^(n+1)/a(n) = 7*Pi^2/3 + 40484864*log(2)/6435 - 10165792859017/2318916600. (End)

Mathematica

Table[15 (n + 1) Binomial[n + 2, 15]/2, {n, 13, 40}] (* or *) Table[Binomial[n + 1, 14] Binomial[n + 2, 2], {n, 13, 40}] (* Michael De Vlieger, Mar 16 2016 *)
LinearRecurrence[{17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1}, {105, 1800, 16320, 104040, 523260, 2209320, 8139600, 26860680, 80901810, 225544440, 588376800, 1448655000, 3389852700, 7582037400, 16287339600, 33738060600, 67621543875}, 30] (* Harvey P. Dale, Jan 12 2023 *)

Crossrefs

Sequence in context: A076377 A165374 A024198 * A112497 A220822 A166821

Adjacent sequences: A027785 A027786 A027787 * A027789 A027790 A027791

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved