OFFSET
8,1
COMMENTS
Number of 17-subsequences of [ 1, n ] with just 4 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 8..1000
Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
FORMULA
G.f.: 55*(9+4*x)*x^8/(1-x)^14.
a(n) = C(n+1, 9)*C(n+4, 4). - Zerinvary Lajos, May 26 2005
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=8} 1/a(n) = 6*Pi^2 - 631959059/10672200.
Sum_{n>=8} (-1)^n/a(n) = 3*Pi^2 + 77824*log(2)/385 - 1811284381/10672200. (End)
MATHEMATICA
Table[55(n+1)Binomial[n+4, 12], {n, 8, 30}] (* or *) CoefficientList[ Series[(55(4x+9))/(x-1)^14, {x, 0, 22}], x] (* Harvey P. Dale, Nov 20 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved