OFFSET
6,1
COMMENTS
Number of 15-subsequences of [ 1, n ] with just 4 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 6..1000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
G.f.: 30*(7+4x)*x^6/(1-x)^12.
a(n) = C(n+1, 7)*C(n+4, 4). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 13 2016
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=6} 1/a(n) = 14*Pi^2/3 - 10444807/226800.
Sum_{n>=6} (-1)^n/a(n) = 7*Pi^2/3 + 3584*log(2)/45 - 2534651/32400. (End)
MATHEMATICA
Table[30 * (n+1) * Binomial[n+4, 10], {n, 6, 50}] (* Amiram Eldar, Feb 03 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved