OFFSET
0,2
COMMENTS
This is row/column 8 of the Delannoy numbers array, A008288, which is the main entry for these numbers, listing many more properties. - Shel Kaphan, Jan 06 2023
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
FORMULA
G.f.: (1+x)^8/(1-x)^9.
First differences of A099196. - Alexander Adamchuk, May 23 2006
a(n) = (2*n^8 + 8*n^7 + 84*n^6 + 224*n^5 + 798*n^4 + 1232*n^3 + 1636*n^2 + 1056*n + 315)/315. - Alexander Adamchuk, May 23 2006
Sum_{n >= 1} (-1)^(n+1)/(n*a(n-1)*a(n)) = log(2) - (1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8). - Peter Bala, Mar 23 2024
MATHEMATICA
CoefficientList[Series[-(z + 1)^8/(z - 1)^9, {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 17, 145, 833, 3649, 13073, 40081, 108545, 265729}, 40] (* Harvey P. Dale, May 26 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Alexander Adamchuk, May 23 2006
STATUS
approved