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A153273
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A Gamma function-based triangular sequence: t(n,m)=m^(n + 1)*Gamma[n + (2*m - 1)/m]/Gamma[(m - 1)/m].
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0
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1, 2, 10, 3, 21, 231, 4, 36, 504, 9576, 5, 55, 935, 21505, 623645, 6, 78, 1560, 42120, 1432080, 58715280, 7, 105, 2415, 74865, 2919735, 137227545, 7547514975, 8, 136, 3536, 123760, 5445440, 288608320, 17893715840, 1270453824640, 9, 171, 4959
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums are:
{1, 12, 255, 10120, 646145, 60191124, 7687739647, 1288641721680,
274338952977249, 72299818200530140}
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FORMULA
| t(n,m)=m^(n + 1)*Gamma[n + (2*m - 1)/m]/Gamma[(m - 1)/m].
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EXAMPLE
| {1},
{2, 10},
{3, 21, 231},
{4, 36, 504, 9576},
{5, 55, 935, 21505, 623645},
{6, 78, 1560, 42120, 1432080, 58715280},
{7, 105, 2415, 74865, 2919735, 137227545, 7547514975},
{8, 136, 3536, 123760, 5445440, 288608320, 17893715840, 1270453824640},
{9, 171, 4959, 193401, 9476649, 559122291, 38579438079, 3047775608241, 271252029133449},
{10, 210, 6720, 288960, 15603840, 1014249600, 77082969600, 6706218355200, 657209398809600, 71635824470246400}
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MATHEMATICA
| t[n_, m_] = m^(n + 1)*Gamma[n + (2*m - 1)/m]/Gamma[(m - 1)/m];
Table[Table[FullSimplify[t[n, m]], {n, 0, m - 2}], {m, 2, 11}];
Flatten[%]
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CROSSREFS
| Sequence in context: A061196 A176577 A120862 * A102512 A196364 A029673
Adjacent sequences: A153270 A153271 A153272 * A153274 A153275 A153276
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 22 2008
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