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A155744
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A symmetrical triangle sequence: t(n,m)=((-1)^(n - m)*StirlingS1[n, m] + (-1)^m*StirlingS1[n, n - m]) + ((-1)^(n - m)*StirlingS1[n, m]*(-1)^(-m)*StirlingS1[n, n - m]).
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0
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3, 1, 1, 1, 3, 1, 1, 11, 11, 1, 1, 48, 143, 48, 1, 1, 274, 1835, 1835, 274, 1, 1, 1935, 23649, 51075, 23649, 1935, 1, 1, 15861, 310639, 1195999, 1195999, 310639, 15861, 1, 1, 146188, 4221286, 25753812, 45832899, 25753812, 4221286, 146188, 1, 1, 1491876
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are:
{3, 2, 5, 24, 241, 4220, 102245, 3045000, 106075473, 4215832488, 188104953945,...}.
There is a similarity here between this triangle sequence
and the Narayana numbers A001263.
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FORMULA
| t(n,m)=((-1)^(n - m)*StirlingS1[n, m] + (-1)^m*StirlingS1[n, n - m]) + ((-1)^(n - m)*StirlingS1[n, m]*(-1)^(-m)*StirlingS1[n, n - m]).
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EXAMPLE
| {3},
{1, 1},
{1, 3, 1},
{1, 11, 11, 1},
{1, 48, 143, 48, 1},
{1, 274, 1835, 1835, 274, 1},
{1, 1935, 23649, 51075, 23649, 1935, 1},
{1, 15861, 310639, 1195999, 1195999, 310639, 15861, 1},
{1, 146188, 4221286, 25753812, 45832899, 25753812, 4221286, 146188, 1},
{1, 1491876, 59942994, 535933124, 1510548249, 1510548249, 535933124, 59942994, 1491876, 1},
{1, 16692525, 894148566, 11083197150, 45790191593, 72536494275, 45790191593, 11083197150, 894148566, 16692525, 1}
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MATHEMATICA
| Clear[t, n, m, a];
t[n_, m_] = ((-1)^(n - m)*StirlingS1[n, m] + (-1)^m*StirlingS1[n, n - m]) + ((-1)^(n - m)*StirlingS1[n, m]*(-1)^(-m)*StirlingS1[n, n - m]);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| A001263
Sequence in context: A087612 A155828 A051997 * A086869 A095345 A132468
Adjacent sequences: A155741 A155742 A155743 * A155745 A155746 A155747
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 26 2009
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