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A157640
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A q-combination triangle sequence :m=2; t(n,k)=If[m == 0, n!, Product[Sum[k*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].
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0
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1, 1, 1, 1, 8, 1, 1, 39, 39, 1, 1, 160, 780, 160, 1, 1, 605, 12100, 12100, 605, 1, 1, 2184, 165165, 677600, 165165, 2184, 1, 1, 7651, 2088723, 32401985, 32401985, 2088723, 7651, 1, 1, 26240, 25095280, 1405335680, 5313925540, 1405335680, 25095280
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, 10, 80, 1102, 25412, 1012300, 68996720, 8174839942, 1670428649564,
594362629986268,...}.
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FORMULA
| m=2; t(n,k)=If[m == 0, n!, Product[Sum[k*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];
b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].
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EXAMPLE
| {1},
{1, 1},
{1, 8, 1},
{1, 39, 39, 1},
{1, 160, 780, 160, 1},
{1, 605, 12100, 12100, 605, 1},
{1, 2184, 165165, 677600, 165165, 2184, 1},
{1, 7651, 2088723, 32401985, 32401985, 2088723, 7651, 1},
{1, 26240, 25095280, 1405335680, 5313925540, 1405335680, 25095280, 26240, 1},
{1, 88569, 290506320, 56991380880, 777932349012, 777932349012, 56991380880, 290506320, 88569, 1},
{1, 295240, 3268638945, 2199207331200, 105163345568820, 379630986317856, 105163345568820, 2199207331200, 3268638945, 295240, 1}
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MATHEMATICA
| t[n_, m_] = If[m == 0, n!, Product[Sum[k*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];
b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];
Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}]
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CROSSREFS
| Sequence in context: A156137 A152972 A166346 * A142458 A174528 A176227
Adjacent sequences: A157637 A157638 A157639 * A157641 A157642 A157643
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 03 2009
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