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Search: id:A156528
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| A156528 |
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A triangular sequence: t(n,m)=(-1)^n*Sum[(-1)^(m - i)*Binomial[n - i - 1, m - i]*StirlingS1[n + i + 1, i + 1], {i, 0, n}]. |
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1
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| 1, 1, 3, 2, 9, 35, 6, 38, 181, 735, 24, 202, 1148, 5395, 22449, 120, 1284, 8560, 45832, 213529, 902055, 720, 9468, 73052, 440516, 2275270, 10540509, 44990231, 5040, 79344, 700380, 4713740, 26783190, 135134070, 623527389, 2681453775, 40320
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums are:
{1, 4, 46, 960, 29218, 1171380, 58329766, 3472396928, 240584307106,
19018858710852, 1689457066042590}
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FORMULA
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t(n,m)=(-1)^n*Sum[(-1)^(m - i)*Binomial[n - i - 1, m - i]*StirlingS1[n + i + 1, i + 1], {i, 0, n}].
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EXAMPLE
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{1},
{1, 3},
{2, 9, 35},
{6, 38, 181, 735},
{24, 202, 1148, 5395, 22449},
{120, 1284, 8560, 45832, 213529, 902055},
{720, 9468, 73052, 440516, 2275270, 10540509, 44990231},
{5040, 79344, 700380, 4713740, 26783190, 135134070, 623527389, 2681453775},
{40320, 744336, 7440840, 55477636, 344589972, 1883062894, 9345564224, 42994209331, 185953177553},
{362880, 7725600, 86678136, 711387192, 4804798156, 28306022216, 150469912896, 737690211448, 3386028203405, 14710753408923},
{3628800, 87884640, 1097845632, 9863244552, 72108611456, 456146630800, 2587934993000, 13476479586304, 65448246877514, 299870086199497, 1307535010540395}
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MATHEMATICA
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Clear[t, n, m, i];
t[n_, m_] = (-1)^n*Sum[(-1)^(m - i)*Binomial[n - i - 1, m - i]*StirlingS1[n + i + 1, i + 1], {i, 0, n}];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A088634 A118791 A049971 this_sequence A092502 A135515 A114486
Adjacent sequences: A156525 A156526 A156527 this_sequence A156529 A156530 A156531
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 09 2009
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