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A158116
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Triangle sequence of general q-combinations: m=2; t(n,m)=t[n_, m_] = If[m == 0, n!, Product[((m + 1)*((m + 1) + 1)/2)^k, {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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2
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1, 1, 1, 1, 6, 1, 1, 36, 36, 1, 1, 216, 1296, 216, 1, 1, 1296, 46656, 46656, 1296, 1, 1, 7776, 1679616, 10077696, 1679616, 7776, 1, 1, 46656, 60466176, 2176782336, 2176782336, 60466176, 46656, 1, 1, 279936, 2176782336, 470184984576
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, 8, 74, 1730, 95906, 13452482, 4474590338, 3765834001154,
7515593525150210, 37950930250093661186,...}.
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FORMULA
| m=2;
t(n,m)=t[n_, m_] = If[m == 0, n!, Product[((m + 1)*((m + 1) + 1)/2)^k, {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, 6, 1},
{1, 36, 36, 1},
{1, 216, 1296, 216, 1},
{1, 1296, 46656, 46656, 1296, 1},
{1, 7776, 1679616, 10077696, 1679616, 7776, 1},
{1, 46656, 60466176, 2176782336, 2176782336, 60466176, 46656, 1},
{1, 279936, 2176782336, 470184984576, 2821109907456, 470184984576, 2176782336, 279936, 1},
{1, 1679616, 78364164096, 101559956668416, 3656158440062976, 3656158440062976, 101559956668416, 78364164096, 1679616, 1},
{1, 10077696, 2821109907456, 21936950640377856, 4738381338321616896, 28430288029929701376, 4738381338321616896, 21936950640377856, 2821109907456, 10077696, 1}
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MATHEMATICA
| t[n_, m_] = If[m == 0, n!, Product[((m + 1)*((m + 1) + 1)/2)^k, {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
| A118180
Sequence in context: A156601 A178232 A203338 * A172343 A058875 A156764
Adjacent sequences: A158113 A158114 A158115 * A158117 A158118 A158119
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 12 2009
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