login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..35.

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

Adjacent sequences:  A027855 A027856 A027857 * A027859 A027860 A027861

KEYWORD

nonn,tabl,easy

AUTHOR

Leroy Quet.

EXTENSIONS

Revised and more terms from Sean A. Irvine, Dec 07 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 2 07:52 EDT 2021. Contains 346411 sequences. (Running on oeis4.)