A222060 Triangle read by rows: coefficients of harmonic-geometric polynomials.

0, 0, 1, 0, 1, 3, 0, 1, 9, 11, 0, 1, 21, 66, 50, 0, 1, 45, 275, 500, 274, 0, 1, 93, 990, 3250, 4110, 1764, 0, 1, 189, 3311, 17500, 38360, 37044, 13068, 0, 1, 381, 10626, 85050, 287700, 469224, 365904, 109584, 0, 1, 765, 33275, 388500, 1904574, 4667544, 6037416, 3945024, 1026576, 0, 1, 1533, 102630, 1705250, 11651850, 40266828, 76839840, 82188000, 46195920, 10628640

Offset

0,6

Links

Table of n, a(n) for n=0..65.

Ayhan Dil and Veli Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series I, INTEGERS, 12 (2012), #A38.

Formula

The n-th polynomial is Sum_{k=0..n} Stirling2(n,k)*|Stirling1(k+1,2)|*x^k.

Example

Triangle begins:
[0]
[0, 1]
[0, 1, 3]
[0, 1, 9, 11]
[0, 1, 21, 66, 50]
[0, 1, 45, 275, 500, 274]
[0, 1, 93, 990, 3250, 4110, 1764]
[0, 1, 189, 3311, 17500, 38360, 37044, 13068]
[0, 1, 381, 10626, 85050, 287700, 469224, 365904, 109584]
...

Crossrefs

Row sums give A222058. See A222057 for another version.

Sequence in context: A152150 A136239 A225443 * A256549 A211608 A058175

Adjacent sequences: A222057 A222058 A222059 * A222061 A222062 A222063

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 08 2013

Status

approved