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A027858
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Triangle of "Harmonic Coefficients" T(n,k), read by rows: (Sum_{i=1..n} T(n,i) * k^i) * k! / ((n+k)! * n!) = (Sum_{i=1..k} (1/i-1/(i+n)) = n * (Sum_{i=1..k} 1/(i*(i+n)))).
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0
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1, 5, 3, 49, 48, 11, 820, 1030, 404, 50, 21076, 31050, 16090, 3510, 274, 773136, 1277136, 792540, 233100, 32724, 1764, 38402064, 69261696, 48943692, 17498880, 3361176, 330624, 13068, 2483133696, 4805827776, 3752675136, 1545593616, 364984704, 49672224, 3622464, 109584
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OFFSET
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0,2
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LINKS
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FORMULA
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T(n, m) = n! * Sum_{k=1..m} ((-1)^(k+1) * S(n+1, m+1-k) * Sum_{i=1..n} i^(-k-1)), where S(n, m) are the unsigned Stirling numbers of the first kind.
T(n, m) = n! * (S(n+1, m+1) * Sum_{k=1..n} (1/k) - S(n+1, m+2)*(m+1)).
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EXAMPLE
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Triangle begins:
1;
5, 3;
49, 48, 11;
820, 1030, 404, 50;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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