OFFSET
7,1
COMMENTS
Number of 18-subsequences of [ 1, n ] with just 5 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 7..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.: 99*(8+5x)*x^7/(1-x)^14.
a(n) = C(n+1, 8)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=7} 1/a(n) = 1263990883/19209960 - 20*Pi^2/3.
Sum_{n>=7} (-1)^(n+1)/a(n) = 10*Pi^2/3 + 69632*log(2)/693 - 1969871597/19209960. (End)
MATHEMATICA
Table[99(n+1)Binomial[n+5, 12], {n, 7, 30}] (* Harvey P. Dale, Dec 05 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved