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1, 1, 1, 2, 1, 3, 6, 2, 3, 13, 24, 6, 6, 13, 71, 120, 24, 18, 26, 71, 461, 720, 120, 72, 78, 142, 461, 3447, 5040, 720, 360, 312, 426, 922, 3447, 29093, 40320, 5040, 2160, 1560, 1704, 2766, 6894, 29093, 273343, 362880, 40320, 15120, 9360, 8520, 11064, 20682
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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FORMULA
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Row sums: Sum_{k=0..n} T(n,k) = A000142(n+1) = (n+1)!.
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EXAMPLE
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The triangle starts at row n=0 with columns 0 <= k <= n:
1;
1, 1;
2, 1, 3;
6, 2, 3, 13;
24, 6, 6, 13, 71;
120, 24, 18, 26, 71, 461;
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MATHEMATICA
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(* b = A003319 *) b[0]=0; b[n_] := b[n] = n! - Sum[k!*b[n-k], {k, 1, n-1}];
T[n_, k_] := (n-k)! b[k+1]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 18 2018 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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