OFFSET
5,1
COMMENTS
Number of 14-subsequences of [ 1, n ] with just 4 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 5..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
G.f.: 42*(3+2x)*x^5/(1-x)^11.
a(n) = C(n+1, 6)*C(n+4, 4). - Zerinvary Lajos, May 25 2005; corrected by R. J. Mathar, Feb 13 2016
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=5} 1/a(n) = 1160923/29400 - 4*Pi^2.
Sum_{n>=5} (-1)^(n+1)/a(n) = 2*Pi^2 + 1536*log(2)/35 - 491481/9800. (End)
MATHEMATICA
Table[21(n+1)Binomial[n+4, 9], {n, 5, 30}] (* Harvey P. Dale, Sep 19 2011 *)
PROG
(PARI) a(n)=21*(n+1)*binomial(n+4, 9) \\ Charles R Greathouse IV, Sep 19 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved