OFFSET
1,1
COMMENTS
Number of 14-subsequences of [ 1, n ] with just 6 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = 7*A052181(n).
G.f.: 7*(1+3*x)*x/(1-x)^9.
a(n) = C(n+1,2)*C(n+6,6). - Zerinvary Lajos, May 26 2005
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=1} 1/a(n) = 5969/300 - 2*Pi^2.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2 - 384*log(2)/5 + 13049/300. (End)
MATHEMATICA
Table[7*(n + 1)*Binomial[n + 6, 7]/2, {n, 1, 50}] (* Amiram Eldar, Feb 03 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved