OFFSET
2,1
COMMENTS
Number of 13-subsequences of [ 1, n ] with just 5 contiguous pairs.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 2..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
G.f.: 7*(3+5x)*x^2/(1-x)^9.
a(n) = C(n+1, 3)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=2} 1/a(n) = 5*Pi^2/2 - 5909/240.
Sum_{n>=2} (-1)^n/a(n) = 5*Pi^2/4 - 32*log(2) + 791/80. (End)
MATHEMATICA
Table[7 * (n+1) * Binomial[n+5, 7], {n, 2, 50}] (* Amiram Eldar, Feb 04 2022 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {21, 224, 1260, 5040, 16170, 44352, 108108, 240240, 495495}, 30] (* Harvey P. Dale, Aug 01 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved