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A158117
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Triangle sequence of general q-combinations: m=3; 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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0
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1, 1, 1, 1, 10, 1, 1, 100, 100, 1, 1, 1000, 10000, 1000, 1, 1, 10000, 1000000, 1000000, 10000, 1, 1, 100000, 100000000, 1000000000, 100000000, 100000, 1, 1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1, 1
(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, 12, 202, 12002, 2020002, 1200200002, 2020002000002, 12002000020000002,
202000200000200000002, 12002000020000002000000002,...}.
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FORMULA
| m=3;
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, 10, 1},
{1, 100, 100, 1},
{1, 1000, 10000, 1000, 1},
{1, 10000, 1000000, 1000000, 10000, 1},
{1, 100000, 100000000, 1000000000, 100000000, 100000, 1},
{1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1},
{1, 10000000, 1000000000000, 1000000000000000, 10000000000000000, 1000000000000000, 1000000000000, 10000000, 1},
{1, 100000000, 100000000000000, 1000000000000000000, 100000000000000000000, 100000000000000000000, 1000000000000000000, 100000000000000, 100000000, 1},
{1, 1000000000, 10000000000000000, 1000000000000000000000, 1000000000000000000000000, 10000000000000000000000000, 1000000000000000000000000, 1000000000000000000000, 10000000000000000, 1000000000, 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: A160562 A176243 A022173 * A172378 A015124 A156767
Adjacent sequences: A158114 A158115 A158116 * A158118 A158119 A158120
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 12 2009
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