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Search: id:A123146
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| A123146 |
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Sum of integers triangular array based on trinomial: trinomial[n,k,m]=(n*(n+1)/2)!/(k!*m!*Abs[k+m-(n*(n+1)/2)]!) where k=1. |
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+0
1
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| 1, 1, 1, 3, 6, 3, 6, 30, 60, 60, 10, 90, 360, 840, 1260, 15, 210, 1365, 5460, 15015, 30030, 21, 420, 3990, 23940, 101745, 325584, 813960, 28, 756, 9828, 81900, 491400, 2260440, 8288280, 24864840, 36, 1260, 21420, 235620, 1884960, 11686752
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Three states with the first state always one: Quadratic Generalization: t[n_, m_] = (a0*n^2+b0*n+c0)!/(m!*(Abs[m + 1 - (a0*n^2+b0*n+c0)])!)
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FORMULA
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a(n,m) = (n*(n+1)/2)!/(m!*Abs[1+m-(n*(n+1)/2)]!)
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EXAMPLE
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1
1, 1
3, 6, 3
6, 30, 60, 60
10, 90, 360, 840, 1260
15, 210, 1365, 5460, 15015, 30030
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MATHEMATICA
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t[n_, m_] = (n*(n + 1)/2)!/(m!*(Abs[m + 1 - (n*(n + 1)/2)])!) a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}] Flatten[a]
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CROSSREFS
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Adjacent sequences: A123143 A123144 A123145 this_sequence A123147 A123148 A123149
Sequence in context: A124860 A038138 A010704 this_sequence A016661 A135003 A090895
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 01 2006
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