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A008969
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Triangle of differences of reciprocals of unity.
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16
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1, 1, 3, 1, 11, 7, 1, 50, 85, 15, 1, 274, 1660, 575, 31, 1, 1764, 48076, 46760, 3661, 63, 1, 13068, 1942416, 6998824, 1217776, 22631, 127, 1, 109584, 104587344, 1744835904, 929081776, 30480800, 137845, 255, 1, 1026576, 7245893376, 673781602752, 1413470290176, 117550462624, 747497920, 833375, 511
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listen;
history;
text;
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OFFSET
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1,3
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
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LINKS
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EXAMPLE
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Triangle T(n,k) begins:
1;
1, 3;
1, 11, 7;
1, 50, 85, 15;
1, 274, 1660, 575, 31;
1, 1764, 48076, 46760, 3661, 63;
1, 13068, 1942416, 6998824, 1217776, 22631, 127;
1, 109584, 104587344, 1744835904, 929081776, 30480800, 137845, 255;
...
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MAPLE
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T:= (n, k)-> `if`(k<=n, (n-k+2)!^k *
add((-1)^(j+1)*binomial(n-k+2, j)/ j^k, j=1..n-k+2), 0):
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MATHEMATICA
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T[n_, k_] := If[k <= n, (n-k+2)!^k*Sum[(-1)^(j+1)*Binomial[n-k+2, j]/j^k, {j, 1, n-k+2}], 0]; Table[Table[T[n, k], {k, 0, n}], {n, 0, 7}] // Flatten (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *)
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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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