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A027858 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)))). 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

FORMULA

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)).

CROSSREFS

Sequence in context: A187278 A288184 A323779 * A181755 A007299 A257935

Adjacent sequences:  A027855 A027856 A027857 * A027859 A027860 A027861

KEYWORD

nonn,tabl,easy

AUTHOR

Leroy Quet.

STATUS

approved

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Last modified March 23 09:20 EDT 2019. Contains 321424 sequences. (Running on oeis4.)