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Search: id:A154843
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| A154843 |
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Symmetrical triangular sequence of Stirling numbers (A048994) of the first kind: t(n,m)=StirlingS1[n, m] + StirlingS1[n, n - m]. |
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1
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| 2, 1, 1, 1, -2, 1, 1, -1, -1, 1, 1, -12, 22, -12, 1, 1, 14, -15, -15, 14, 1, 1, -135, 359, -450, 359, -135, 1, 1, 699, -1589, 889, 889, -1589, 699, 1, 1, -5068, 13390, -15092, 13538, -15092, 13390, -5068, 1, 1, 40284, -109038, 113588, -44835, -44835, 113588
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Except for the first two the row sums are zero.
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FORMULA
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t(n,m)=StirlingS1[n, m] + StirlingS1[n, n - m].
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EXAMPLE
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{2},
{1, 1},
{1, -2, 1},
{1, -1, -1, 1},
{1, -12, 22, -12, 1},
{1, 14, -15, -15, 14, 1},
{1, -135, 359, -450, 359, -135, 1},
{1, 699, -1589, 889, 889, -1589, 699, 1},
{1, -5068, 13390, -15092, 13538, -15092, 13390, -5068, 1},
{1, 40284, -109038, 113588, -44835, -44835, 113588, -109038, 40284, 1},
{1, -362925, 1027446, -1182150, 786953, -538650, 786953, -1182150, 1027446, -362925, 1}
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MATHEMATICA
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Clear[t, n, m]; t[n_, m_] = StirlingS1[n, m] + StirlingS1[n, n - m];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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A048994
Sequence in context: A031230 A111616 A113120 this_sequence A062557 A003649 A003650
Adjacent sequences: A154840 A154841 A154842 this_sequence A154844 A154845 A154846
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 16 2009
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