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A156766
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A new q-combination type general triangle sequence : here q=3: 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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1, 1, 1, 1, 8, 1, 1, 78, 78, 1, 1, 960, 9360, 960, 1, 1, 14520, 1742400, 1742400, 14520, 1, 1, 262080, 475675200, 5854464000, 475675200, 262080, 1, 1, 5508720, 180465667200, 33594378048000, 33594378048000, 180465667200, 5508720, 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, 10, 158, 11282, 3513842, 6806338562, 67549698447842,
5240105505531187202, 2284774386577649113916162,
9329163681182445949013122406402,...}.
"Wirklich and glaublich, aber is das wichtig?"
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FORMULA
| q=3: 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, 78, 78, 1},
{1, 960, 9360, 960, 1},
{1, 14520, 1742400, 1742400, 14520, 1},
{1, 262080, 475675200, 5854464000, 475675200, 262080, 1},
{1, 5508720, 180465667200, 33594378048000, 33594378048000, 180465667200, 5508720, 1},
{1, 132249600, 91065752064000, 305980926935040000, 4627961519892480000, 305980926935040000, 91065752064000, 132249600, 1},
{1, 3571102080, 59034602704896000, 4169296110416855040000, 1138217838143801425920000, 1138217838143801425920000, 4169296110416855040000, 59034602704896000, 3571102080, 1},
{1, 107136691200, 47824507598579712000, 81086820514219583078400000, 465296447815720522599628800000, 8398408611814327449236275200000, 465296447815720522599628800000, 81086820514219583078400000, 47824507598579712000, 107136691200, 1}
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MATHEMATICA
| Clear[t, n, m, i, k, a, b];
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: A178048 A174728 A015121 * A178046 A176340 A111835
Adjacent sequences: A156763 A156764 A156765 * A156767 A156768 A156769
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 15 2009
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