OFFSET
2,1
COMMENTS
Number of 15-subsequences of [ 1, n ] with just 6 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: 28*(1+2x)*x^2/(1-x)^10.
a(n) = C(n+1, 3)*C(n+6, 6). - Zerinvary Lajos, Jun 08 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=2} 1/a(n) = 3*Pi^2 - 289781/9800.
Sum_{n>=2} (-1)^n/a(n) = 3*Pi^2/2 - 2112*log(2)/35 + 265141/9800. (End)
MATHEMATICA
Table[28(n+1) Binomial[n+6, 8]/3, {n, 2, 30}] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {28, 336, 2100, 9240, 32340, 96096, 252252, 600600, 1321320, 2722720}, 30] (* Harvey P. Dale, Sep 12 2017 *)
PROG
(PARI) a(n)=28*(n+1)*binomial(n+6, 8)/3 \\ Charles R Greathouse IV, May 22 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved