OFFSET
11,1
COMMENTS
Number of 16-subsequences of [ 1, n ] with just 2 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 11..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.: 13*(6+x)*x^11/(1-x)^15.
a(n) = C(n+1, 12)*C(n+2, 2). - Zerinvary Lajos, Apr 28 2005; corrected by R. J. Mathar, Mar 15 2016
From Amiram Eldar, Feb 01 2022: (Start)
Sum_{n>=11} 1/a(n) = 632203177/16008300 - 4*Pi^2.
Sum_{n>=11} (-1)^(n+1)/a(n) = 2*Pi^2 + 2277376*log(2)/1155 - 22194594643/16008300. (End)
MATHEMATICA
Table[13 (n + 1) Binomial[n + 2, 13]/2, {n, 11, 40}] (* Wesley Ivan Hurt, Mar 30 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved