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A213999
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Denominators of the triangle of fractions read by rows: pf(n,0) = 1, pf(n,n) = 1/(n+1) and pf(n+1,k) = pf(n,k) + pf(n,k-1) with 0 < k < n; denominators: A213998.
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11
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1, 1, 2, 1, 2, 3, 1, 2, 6, 4, 1, 2, 3, 12, 5, 1, 2, 6, 12, 60, 6, 1, 2, 3, 4, 10, 20, 7, 1, 2, 6, 12, 20, 20, 140, 8, 1, 2, 3, 12, 15, 10, 35, 280, 9, 1, 2, 6, 4, 20, 30, 70, 280, 2520, 10, 1, 2, 3, 12, 10, 12, 21, 56, 252, 2520, 11, 1, 2, 6, 12, 60, 60, 84, 168, 504, 2520, 27720, 12
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OFFSET
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0,3
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COMMENTS
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T(n,0) = 1;
T(n,n) = n + 1;
A003418(n+1) = least common multiple of n-th row;
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LINKS
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EXAMPLE
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MATHEMATICA
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T[_, 0] = 1; T[n_, n_] := 1/(n + 1);
T[n_, k_] := T[n, k] = T[n - 1, k] + T[n - 1, k - 1];
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PROG
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(Haskell)
import Data.Ratio ((%), denominator, Ratio)
a213999 n k = a213999_tabl !! n !! k
a213999_row n = a213999_tabl !! n
a213999_tabl = map (map denominator) $ iterate pf [1] where
pf row = zipWith (+) ([0] ++ row) (row ++ [-1 % (x * (x + 1))])
where x = denominator $ last row
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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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