A373717 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..floor(k*n/(2*k+1))} binomial(k * (n-2*j),j).
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 4, 5, 4, 1, 1, 1, 1, 5, 7, 8, 6, 1, 1, 1, 1, 6, 9, 13, 15, 9, 1, 1, 1, 1, 7, 11, 19, 28, 26, 13, 1, 1, 1, 1, 8, 13, 26, 45, 53, 45, 19, 1, 1, 1, 1, 9, 15, 34, 66, 91, 105, 80, 28, 1, 1, 1, 1, 10, 17, 43, 91, 141, 201, 211, 140, 41, 1
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, 1, 1, ... 1, 2, 3, 4, 5, 6, 7, ... 1, 3, 5, 7, 9, 11, 13, ... 1, 4, 8, 13, 19, 26, 34, ... 1, 6, 15, 28, 45, 66, 91, ...
Crossrefs
Programs
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PARI
T(n, k) = sum(j=0, k*n\(2*k+1), binomial(k*(n-2*j), j));
Formula
G.f. of column k: 1/(1 - x * (1 + x^2)^k).
T(n,k) = Sum_{j=0..k} binomial(k,j) * T(n-2*j-1,k).