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Triangle: see Mathematica code.
0

%I #14 Dec 24 2022 05:17:06

%S 1,1,1,1,1,2,1,2,3,6,1,3,40,35,24,1,4,165,8372,1755,120,1,5,456,

%T 159831,17174080,382075,720,1,6,1015,1387064,2572040925,329455658840,

%U 354205467,5040,1,7,1968,7773755,107605514016,670559078523807,57782732285824000,1368556206875,40320

%N Triangle: see Mathematica code.

%e {1},

%e {1, 1},

%e {1, 1, 2},

%e {1, 2, 3, 6},

%e {1, 3, 40, 35, 24},

%e {1, 4, 165, 8372, 1755, 120},

%e {1, 5, 456, 159831, 17174080, 382075, 720},

%e {1, 6, 1015, 1387064, 2572040925, 329455658840, 354205467, 5040},

%t t[n_, m_] = If[m == 0, n!, Product[(m + 1)^n - Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];

%t a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}];

%t b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}];

%t Flatten[%]

%K nonn,tabl,uned,obsc,less

%O 0,6

%A _Roger L. Bagula_ and _Gary W. Adamson_, Feb 10 2009