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A233543
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Table T(n,m) = m! read by rows.
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0
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1, 1, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 2, 6, 24, 1, 1, 2, 6, 24, 120, 1, 1, 2, 6, 24, 120, 720, 1, 1, 2, 6, 24, 120, 720, 5040, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880
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refs;
listen;
history;
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OFFSET
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0,6
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COMMENTS
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1,
1, 1,
1, 2, 2,
1, 2, 3, 3,
1, 2, 3, 4, 4,
1, 2, 3, 4, 5, 5,
1, 2, 3, 4, 5, 6, 6, etc.
The first column of the inverse triangle is
1, -1, 1/2, -1/6, 1/24, -1/120, -1/720,... = 1/e, where e is Euler's number A001113. It is found by
1,
1 - 1 = 0,
1 - 2 + 2/2 = 0,
1 - 2 + 3/2 - 3/6 = 0,
1 - 2 + 3/2 - 4/6 + 4/24 = 0,
1 - 2 + 3/2 - 4/6 + 5/24 - 5/120 = 0,
1 - 2 + 3/2 - 4/6 + 5/24 - 6/120 + 6/720 = 0, etc.
The numerators of this fractional triangle are A193738 signed by rows.
The denominators are a(n).
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LINKS
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FORMULA
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EXAMPLE
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1,
1, 1,
1, 1, 2,
1, 1, 2, 6
1, 1, 2, 6, 24,
1, 1, 2, 6, 24, 120, etc.
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MATHEMATICA
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t[_, m_] := m!; Table[Table[t[n, m], {m, 0, n}], {n, 0, 9}] // Flatten (* Jean-François Alcover, Dec 12 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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