%I #16 Oct 31 2023 11:15:52
%S 1,1,2,1,3,2,1,4,4,3,1,5,7,7,2,1,6,11,14,6,4,1,7,16,25,16,12,2,1,8,22,
%T 41,36,31,8,4,1,9,29,63,71,71,29,15,3,1,10,37,92,127,147,85,50,13,4,1,
%U 11,46,129,211,280,211,145,52,18,2,1,12,56,175,331,498,463,371,176,74,12,6
%N Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{d|n} binomial(d+k-1,k).
%F G.f. of column k: Sum_{j>=1} x^j/(1 - x^j)^(k+1).
%e Square array begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 2, 3, 4, 5, 6, 7, 8, ...
%e 2, 4, 7, 11, 16, 22, 29, ...
%e 3, 7, 14, 25, 41, 63, 92, ...
%e 2, 6, 16, 36, 71, 127, 211, ...
%e 4, 12, 31, 71, 147, 280, 498, ...
%e 2, 8, 29, 85, 211, 463, 925, ...
%o (PARI) T(n, k) = sumdiv(n, d, binomial(d+k-1, k));
%Y Columns k=0..5 give A000005, A000203, A007437, A059358, A073570, A101289.
%Y T(n,n-1) gives A332508.
%Y T(n,n) gives A343548.
%Y Cf. A366977.
%K nonn,tabl
%O 1,3
%A _Seiichi Manyama_, Oct 31 2023