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A156579
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A triangular sequence of the antidiagonal of the backward q squared like factorial: t(n,m)=If[m == 0, n!, Product[Sum[(k - i)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]].
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0
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1, 1, 1, 1, 1, 2, 1, 1, 4, 6, 1, 1, 5, 44, 24, 1, 1, 6, 90, 1144, 120, 1, 1, 7, 162, 5220, 65208, 720, 1, 1, 8, 266, 18144, 934380, 7824960, 5040, 1, 1, 9, 408, 51604, 8219232, 507368340, 1932765120, 40320, 1, 1, 10, 594, 126480, 50313900, 14942563776
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OFFSET
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0,6
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COMMENTS
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Row sums are:
{1, 2, 4, 12, 75, 1362, 71319, 8782800, 2448445035, 1815296062122,
5172422493520011,...}.
Reversed polynomials give this sequence.
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LINKS
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Table of n, a(n) for n=0..51.
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FORMULA
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t(n,m)=If[m == 0, n!, Product[Sum[(k - i)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];
out_(n,m)=antidiagonal(t(n,m))
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EXAMPLE
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{1},
{1, 1},
{1, 1, 2},
{1, 1, 4, 6},
{1, 1, 5, 44, 24},
{1, 1, 6, 90, 1144, 120},
{1, 1, 7, 162, 5220, 65208, 720},
{1, 1, 8, 266, 18144, 934380, 7824960, 5040},
{1, 1, 9, 408, 51604, 8219232, 507368340, 1932765120, 40320},
{1, 1, 10, 594, 126480, 50313900, 14942563776, 830054604240, 970248090240, 362880},
{1, 1, 11, 830, 276804, 235885200, 245582145900, 108766921725504, 4080548434443840, 982861315413120, 3628800}
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MATHEMATICA
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Clear[t, n, m, i, k, a, b];
t[n_, m_] = If[m == 0, n!, Product[Sum[(k - i)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];
a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}];
b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}];
Flatten[%]
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CROSSREFS
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Sequence in context: A307977 A295259 A255009 * A322266 A190284 A327639
Adjacent sequences: A156576 A156577 A156578 * A156580 A156581 A156582
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula, Feb 10 2009
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STATUS
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approved
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