OFFSET
0,8
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
FORMULA
A(n,k) = Sum_{j=0..k*n-1} C(n+2*j-1,2*j), A(0,k) = 1.
A(n,k) = A071921(n,k*n).
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 4, 16, 36, 64, 100, ...
0, 22, 161, 525, 1222, 2360, ...
0, 130, 1716, 8086, 24616, 58730, ...
0, 791, 18832, 128248, 510664, 1505205, ...
MAPLE
A:= (n, k)-> `if`(n=0, 1, add(binomial(n+2*j-1, 2*j), j=0..k*n-1)):
seq(seq(A(n, d-n), n=0..d), d=0..10);
MATHEMATICA
A[n_, k_] := If[n==0, 1, Sum[Binomial[n + 2j - 1, 2j], {j, 0, k n - 1}]];
Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 10}] // Flatten (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, May 23 2013
STATUS
approved