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A130671
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Triangular sequence based on Pascal's triangle: t(n,m) = 2*binomial(m, n) - (1 + n*(m - n)).
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0
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 13, 5, 1, 1, 6, 21, 30, 21, 6, 1, 1, 7, 31, 57, 57, 31, 7, 1, 1, 8, 43, 96, 123, 96, 43, 8, 1, 1, 9, 57, 149, 231, 231, 149, 57, 9, 1, 1, 10, 73, 218, 395, 478, 395, 218, 73, 10, 1
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OFFSET
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1,5
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COMMENTS
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Suggested by Gary W. Adamson from a previous submission. Very close to (but slightly smaller at 7th row) A086617.
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LINKS
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FORMULA
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t(n,m) = 2*binomial[m, n] - (1 + n*(m - n)).
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EXAMPLE
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{1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 4, 7, 4, 1},
{1, 5, 13, 13, 5, 1},
{1, 6, 21, 30, 21, 6, 1},
{1, 7, 31, 57, 57, 31, 7, 1}
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MATHEMATICA
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Table[Table[2*Binomial[m, n] - (1 + n*(m - n)), {n, 0, m}], {m, 0, 10}] Flatten[%]
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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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