OFFSET
12,1
COMMENTS
Number of 17-subsequences of [ 1, n ] with just 2 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 12..1000
Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
FORMULA
G.f.: 7*(13+2x)*x^12/(1-x)^16.
a(n) = C(n+1, 13)*C(n+2, 2). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Mar 16 2016
From Amiram Eldar, Feb 01 2022: (Start)
Sum_{n>=12} 1/a(n) = 13*Pi^2/3 - 106775635663/2497294800.
Sum_{n>=12} (-1)^n/a(n) = 13*Pi^2/6 + 12132352*log(2)/3465 - 6114275457217/2497294800. (End)
MATHEMATICA
Table[7(n+1)Binomial[n+2, 14], {n, 12, 40}] (* Harvey P. Dale, Jul 18 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
EXTENSIONS
Offset corrected by Harvey P. Dale, Jul 18 2011
STATUS
approved