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A174691
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A symmetrical triangle sequence: t(n,m)=n!*Eulerian[n + 1, m] - n! + 1
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0
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1, 1, 1, 1, 7, 1, 1, 61, 61, 1, 1, 601, 1561, 601, 1, 1, 6721, 36121, 36121, 6721, 1, 1, 85681, 856801, 1738801, 856801, 85681, 1, 1, 1239841, 21631681, 78714721, 78714721, 21631681, 1239841, 1, 1, 20200321, 588954241, 3557554561, 6297540481
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OFFSET
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0,5
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COMMENTS
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Row sums are:
{1, 2, 9, 124, 2765, 85686, 3623767, 203172488, 14630958729, 1316815315210,
144850043923211,...}.
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LINKS
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FORMULA
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t(n,m)=n!*Eulerian[n + 1, m] - n! + 1
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EXAMPLE
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{1},
{1, 1},
{1, 7, 1},
{1, 61, 61, 1},
{1, 601, 1561, 601, 1},
{1, 6721, 36121, 36121, 6721, 1},
{1, 85681, 856801, 1738801, 856801, 85681, 1},
{1, 1239841, 21631681, 78714721, 78714721, 21631681, 1239841, 1},
{1, 20200321, 588954241, 3557554561, 6297540481, 3557554561, 588954241, 20200321, 1},
{1, 367234561, 17359816321, 165179710081, 475500896641, 475500896641, 165179710081, 17359816321, 367234561, 1},
{1, 7384608001, 553885516801, 7996013625601, 35337664454401, 57060147513601, 35337664454401, 7996013625601, 553885516801, 7384608001, 1}
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MATHEMATICA
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<< DiscreteMath`Combinatorica`
t[n_, m_] = n!*Eulerian[n + 1, m] - n! + 1;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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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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