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A027858 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)))). 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
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)).
EXAMPLE
Triangle begins:
1;
5, 3;
49, 48, 11;
820, 1030, 404, 50;
...
CROSSREFS
Sequence in context: A288184 A323779 A343290 * A181755 A007299 A257935
KEYWORD
nonn,tabl,easy
AUTHOR
EXTENSIONS
Revised and more terms from Sean A. Irvine, Dec 07 2019
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)