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A157641
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A q-combination triangle sequence :m=3; 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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1, 1, 1, 1, 10, 1, 1, 63, 63, 1, 1, 340, 2142, 340, 1, 1, 1705, 57970, 57970, 1705, 1, 1, 8190, 1396395, 7536100, 1396395, 8190, 1, 1, 38227, 31307913, 847301455, 847301455, 31307913, 38227, 1, 1, 174760, 668055052, 86847156760, 435512947870
(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, 128, 2824, 119352, 10345272, 1757295192, 610543721016,
418465696229912, 584788183756728952,...}.
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FORMULA
| m=3; 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, 10, 1},
{1, 63, 63, 1},
{1, 340, 2142, 340, 1},
{1, 1705, 57970, 57970, 1705, 1},
{1, 8190, 1396395, 7536100, 1396395, 8190, 1},
{1, 38227, 31307913, 847301455, 847301455, 31307913, 38227, 1},
{1, 174760, 668055052, 86847156760, 435512947870, 86847156760, 668055052, 174760, 1},
{1, 786429, 13743633204, 8339331214116, 200879772481206, 200879772481206, 8339331214116, 13743633204, 786429, 1},
{1, 3495250, 274876596225, 762498951687000, 85729551253349850, 411803533586472300, 85729551253349850, 762498951687000, 274876596225, 3495250, 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: A171692 A152971 A142459 * A129274 A176021 A166972
Adjacent sequences: A157638 A157639 A157640 * A157642 A157643 A157644
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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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