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A156767
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A new q-combination type general triangle sequence : here q=4: 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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0
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1, 1, 1, 1, 10, 1, 1, 126, 126, 1, 1, 2040, 25704, 2040, 1, 1, 40920, 8347680, 8347680, 40920, 1, 1, 982800, 4021617600, 65111904000, 4021617600, 982800, 1, 1, 27523440, 2705003683200, 878482148544000, 878482148544000, 2705003683200, 27523440, 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, 254, 29786, 16777202, 73157104802, 1762374359501282,
417116416427546976002, 589047470776461919460232962,
9868826688065727016444829530560002,...}.
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FORMULA
| q=4: 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, 126, 126, 1},
{1, 2040, 25704, 2040, 1},
{1, 40920, 8347680, 8347680, 40920, 1},
{1, 982800, 4021617600, 65111904000, 4021617600, 982800, 1},
{1, 27523440, 2705003683200, 878482148544000, 878482148544000, 2705003683200, 27523440, 1},
{1, 880790400, 2424238172697600, 18909057747041280000, 379293452455357440000, 18909057747041280000, 2424238172697600, 880790400, 1},
{1, 31708817280, 2792882185557811200, 610077184613248278528000, 293913655410735494184960000, 293913655410735494184960000, 610077184613248278528000, 2792882185557811200, 31708817280, 1},
{1, 1268356320000, 4021807879681320960000, 28114045802124306038784000000, 379311398427460887156916224000000, 9110147663111157377757020160000000, 379311398427460887156916224000000, 28114045802124306038784000000, 4021807879681320960000, 1268356320000, 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: A158117 A172378 A015124 * A174921 A010180 A109013
Adjacent sequences: A156764 A156765 A156766 * A156768 A156769 A156770
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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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