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A366986 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).

%I A366986 #16 Oct 31 2023 11:15:52
%S A366986 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 A366986 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 A366986 11,46,129,211,280,211,145,52,18,2,1,12,56,175,331,498,463,371,176,74,12,6
%N A366986 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 A366986 G.f. of column k: Sum_{j>=1} x^j/(1 - x^j)^(k+1).
%e A366986 Square  array begins:
%e A366986   1,  1,  1,  1,   1,   1,   1, ...
%e A366986   2,  3,  4,  5,   6,   7,   8, ...
%e A366986   2,  4,  7, 11,  16,  22,  29, ...
%e A366986   3,  7, 14, 25,  41,  63,  92, ...
%e A366986   2,  6, 16, 36,  71, 127, 211, ...
%e A366986   4, 12, 31, 71, 147, 280, 498, ...
%e A366986   2,  8, 29, 85, 211, 463, 925, ...
%o A366986 (PARI) T(n, k) = sumdiv(n, d, binomial(d+k-1, k));
%Y A366986 Columns k=0..5 give A000005, A000203, A007437, A059358, A073570, A101289.
%Y A366986 T(n,n-1) gives A332508.
%Y A366986 T(n,n) gives A343548.
%Y A366986 Cf. A366977.
%K A366986 nonn,tabl
%O A366986 1,3
%A A366986 _Seiichi Manyama_, Oct 31 2023