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A064670
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Triangle T(n,k) (1 <= k <= n) where the first column (T(n,1)) is the sequence of secant numbers A000364.
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0
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1, 1, 4, 5, 20, 36, 61, 244, 504, 576, 1385, 5540, 11916, 17280, 14400, 50521, 202084, 442224, 697536, 792000, 518400, 2702765, 10811060, 23870196, 39202560, 50198400, 47174400, 25401600, 199360981, 797443924, 1769923944
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OFFSET
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1,3
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COMMENTS
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Replacing m*m by m*(m+1) in the formula, the first column gives the tangent numbers A000182.
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LINKS
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FORMULA
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T(n+1, m) = m*m*Sum_{k = m-1, n} T(n, k) (T(n, 0) = 0).
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EXAMPLE
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T(4,3) = 9*(T(3,2) + (T(3,3)) = 9*(20+36) = 504.
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MATHEMATICA
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T[1, 1] = 1; T[n_, k_] /; 1 <= k <= n := T[n, k] = k^2*Sum[T[n-1, j], {j, k-1, n-1}]; T[_, _] = 0; Table[T[n, k], {n, 1, 8}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 25 2016 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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Jose L. Arregui (arregui(AT)posta.unizar.es), Oct 09 2001
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EXTENSIONS
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STATUS
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approved
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