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A318255
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Associated Omega numbers of order 3, triangle T(n,k) read by rows for n >= 0 and 0 <= k <= n.
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2
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1, 1, 1, 1, 10, -9, 1, 28, -504, 477, 1, 55, -4158, 78705, -74601, 1, 91, -18018, 1432431, -27154764, 25740261, 1, 136, -55692, 11595870, -923261976, 17503377480, -16591655817, 1, 190, -139536, 60087690, -12529983960, 997692516360, -18914487631380, 17929265150637
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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T(m, n, k) = binomial(m*n-1, m*(n-k))*A318253(m, k) for k>0 and 1 for k=0. We consider here the case m=3.
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EXAMPLE
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Triangle starts:
[0] 1
[1] 1, 1
[2] 1, 10, -9
[3] 1, 28, -504, 477
[4] 1, 55, -4158, 78705, -74601
[5] 1, 91, -18018, 1432431, -27154764, 25740261
[6] 1, 136, -55692, 11595870, -923261976, 17503377480, -16591655817
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MAPLE
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# The function TNum is defined in A318253.
T := (m, n, k) -> `if`(k=0, 1, binomial(m*n-1, m*(n-k))*TNum(m, k)):
for n from 0 to 6 do seq(T(3, n, k), k=0..n) od;
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PROG
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(Sage) # uses[AssociatedOmegaNumberTriangle from A318254]
A318255Triangle = lambda dim: AssociatedOmegaNumberTriangle(3, dim)
print(A318255Triangle(8))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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