OFFSET
0,4
LINKS
S. Corteel, A. Denise, D. Gouyou-Beauchamps, Bijections for directed animals on infinite families of lattices, Ann. Combinat. 4 (3-4) (2000), 269-284, Eq. (5.14).
EXAMPLE
The array starts with rows n>=0 and columns k>=0 as:
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2, 4, 6, 8, 10, 12, 14, 16, 18, ...
4, 19, 46, 85, 136, 199, 274, 361, 460, ...
8, 96, 376, 960, 1960, 3488, 5656, 8576, 12360, ...
16, 501, 3176, 11201, 29176, 63141, 120576, 210401, 342976, ...
32, 2668, 27384, 133400, 443296,1166628,2623544,5268400,9713376, ...
MAPLE
A296129 := proc(n, k)
local a, i, l;
a := 0 ;
for i from 1 to n do
add( binomial(i, l)*binomial((k+1)*l, i-1), l=0..i) ;
a := a+ %*binomial(n-1, i-1)*(i*k+1)/(2*i*(k+1)) ;
end do;
a ;
end proc:
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Dec 05 2017
STATUS
approved