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A157638
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A q-combination triangle sequence :m=1; 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, 6, 1, 1, 21, 21, 1, 1, 60, 210, 60, 1, 1, 155, 1550, 1550, 155, 1, 1, 378, 9765, 27900, 9765, 378, 1, 1, 889, 56007, 413385, 413385, 56007, 889, 1, 1, 2040, 302260, 5440680, 14055090, 5440680, 302260, 2040, 1, 1, 4599, 1563660, 66194940
(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, 8, 44, 332, 3412, 48188, 940564, 25545052, 969582644, 51635485244,...}.
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FORMULA
| m=1; 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, 6, 1},
{1, 21, 21, 1},
{1, 60, 210, 60, 1},
{1, 155, 1550, 1550, 155, 1},
{1, 378, 9765, 27900, 9765, 378, 1},
{1, 889, 56007, 413385, 413385, 56007, 889, 1},
{1, 2040, 302260, 5440680, 14055090, 5440680, 302260, 2040, 1},
{1, 4599, 1563660, 66194940, 417028122, 417028122, 66194940, 1563660, 4599, 1},
{1, 10230, 7841295, 761725800, 11286237270, 27523856052, 11286237270, 761725800, 7841295, 10230, 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: A060972 A144066 A056941 * A142596 A176063 A155467
Adjacent sequences: A157635 A157636 A157637 * A157639 A157640 A157641
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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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