A027785 a(n) = 6*(n+1)*binomial(n+2,12).

66, 936, 7098, 38220, 163800, 594048, 1893528, 5441904, 14360580, 35271600, 81477396, 178474296, 373173528, 748843200, 1448655000, 2711882160, 4928324310, 8718517080, 15049821150, 25401694500, 41997468240, 68124925440, 108574099920, 170228167200, 262852317000

Offset

10,1

Comments

Number of 15-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 10..1000

Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Formula

G.f.: 6*(11+2*x)*x^10/(1-x)^14.

a(n) = C(n+1, 11)*C(n+2, 2). - Zerinvary Lajos, May 13 2005; corrected by R. J. Mathar, Mar 15 2016

From Amiram Eldar, Feb 01 2022: (Start)

Sum_{n>=10} 1/a(n) = 11*Pi^2/3 - 631696027/17463600.

Sum_{n>=10} (-1)^n/a(n) = 11*Pi^2/6 + 354304*log(2)/315 - 13930965493/17463600. (End)

Mathematica

Table[6(n+1)Binomial[n+2, 12], {n, 10, 60}] (* Harvey P. Dale, Jan 03 2018 *)

Prog

(Magma) [6*(n+1)*Binomial(n+2, 12) : n in [10..50]]; // Wesley Ivan Hurt, Apr 20 2021

Crossrefs

Sequence in context: A304838 A337896 A056468 * A271757 A228996 A196789

Adjacent sequences: A027782 A027783 A027784 * A027786 A027787 A027788

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved