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A174555
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Triangle read by rows:s(n,m)=Sum[StirlingS2[n, k]*StirlingS1[n - k, m]* Binomial[n, k]*(-1)^(m - k), {k, 0, n}];t[n,m]=s[n,m]+s[n,n-m]
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0
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2, -1, -1, 1, 4, 1, -1, -15, -15, -1, 1, 78, 108, 78, 1, -1, -635, -935, -935, -635, -1, 1, 7605, 12315, 9600, 12315, 7605, 1, -1, -123396, -225071, -147700, -147700, -225071, -123396, -1, 1, 2570484, 5190598, 3588508, 1936340, 3588508, 5190598
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OFFSET
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0,1
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COMMENTS
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Row sums are:
{2, -2, 6, -32, 266, -3142, 49442, -992336, 24635522, -738902954, 26271105662,...}.
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LINKS
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FORMULA
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s(n,m)=Sum[StirlingS2[n, k]*StirlingS1[n - k, m]* Binomial[n, k]*(-1)^(m - k), {k, 0, n}];
t[n,m]=s[n,m]+s[n,n-m]
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EXAMPLE
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{2},
{-1, -1},
{1, 4, 1},
{-1, -15, -15, -1},
{1, 78, 108, 78, 1},
{-1, -635, -935, -935, -635, -1},
{1, 7605, 12315, 9600, 12315, 7605, 1},
{-1, -123396, -225071, -147700, -147700, -225071, -123396, -1},
{1, 2570484, 5190598, 3588508, 1936340, 3588508, 5190598, 2570484, 1},
{-1, -66359889, -145212474, -112391706, -45487407, -45487407, -112391706, -145212474, -66359889, -1},
{1, 2069254630, 4829689875, 4139150270, 1738086315, 718743480, 1738086315, 4139150270, 4829689875, 2069254630, 1}
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MATHEMATICA
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t[n_, m_] = Sum[StirlingS2[n, k]*StirlingS1[n - k, m]*Binomial[ n, k]*(-1)^(m - k), {k, 0, n}];
Table[Table[t[n, m] + t[n, 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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