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Search: id:A027858
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| A027858 |
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Triangle of "Harmonic Coefficients" T(j,k), read by rows: (sum:n=1 to j: T(j,n)*k^n)*k!/((j+k)!*j!) =(sum:n=1 to k:(1/n-1/(n+j)) =j*(sum:n=1 to k:1/(n*(n+j)))). |
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+0
1
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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
(list; table; graph; listen)
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OFFSET
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0,2
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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T(j, n)=j!*(sum:m=1 to n: S(j+1, n+1-m)*(-1)^(m+1)*(sum:i=1 to j:i^(-m-1))), where S(M, N) is a Stirling number of first kind (unsigned). Also T(j, n)=j!*(S(j+1, n+1)*(1+1/2+1/3+...1/j)-S(j+1, n+2)*(n+1)).
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CROSSREFS
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Sequence in context: A032532 A111108 A038245 this_sequence A124013 A007299 A109254
Adjacent sequences: A027855 A027856 A027857 this_sequence A027859 A027860 A027861
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Leroy Quet.
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