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Search: id:A153187
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| A153187 |
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Triangle sequence: t(n,m)=-Product[m*k - 1, {k, 0, n}]. |
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+0
1
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| 0, 1, 3, 2, 10, 80, 3, 21, 231, 3465, 4, 36, 504, 9576, 229824, 5, 55, 935, 21505, 623645, 21827575, 6, 78, 1560, 42120, 1432080, 58715280, 2818333440, 7, 105, 2415, 74865, 2919735, 137227545, 7547514975, 475493443425, 8, 136, 3536, 123760, 5445440
(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:
{0, 4, 92, 3720, 239944, 22473720, 2878524564, 483181183072, 102924947692880,
27128289837188700,...}
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FORMULA
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t(n,m)=-Product[m*k - 1, {k, 0, n}]; t(n,m)=-m^(n + 1) Pochhammer[ -1/m, 1 + n]; t(n,m)=-m^(n + 1)*Gamma[n + (m - 1)/m]/Gamma[ -1/m].
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EXAMPLE
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{0},
{1, 3},
{2, 10, 80},
{3, 21, 231, 3465},
{4, 36, 504, 9576, 229824},
{5, 55, 935, 21505, 623645, 21827575},
{6, 78, 1560, 42120, 1432080, 58715280, 2818333440},
{7, 105, 2415, 74865, 2919735, 137227545, 7547514975, 475493443425},
{8, 136, 3536, 123760, 5445440, 288608320, 17893715840, 1270453824640, 101636305971200},
{9, 171, 4959, 193401, 9476649, 559122291, 38579438079, 3047775608241, 271252029133449, 26853950884211451}
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MATHEMATICA
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t[n_, m_] = -Product[m*k - 1, {k, 0, n}];
Table[Table[t[n, m], {n, 1, m}], {m, 1, 10}];
Flatten[%]
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CROSSREFS
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A008544
Sequence in context: A096073 A088302 A074199 this_sequence A152177 A110326 A112061
Adjacent sequences: A153184 A153185 A153186 this_sequence A153188 A153189 A153190
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 20 2008
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