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
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved