A222057 Triangle read by rows: coefficients of harmonic-geometric polynomials.

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

Offset: 1

Author

N. J. A. Sloane, Feb 08 2013

Keywords

• nonn
• tabl

Examples

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

Links

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

Crossrefs

Row sums give A222058. See A222060 for another version (including row & column 0).

Programs

PARI

A222057(n,k)=stirling(n,k,2)*abs(stirling(k+1,2)) \\ with 1 <= k <= n: vector(8,n,vector(n,k,A222057(n,k))). - M. F. Hasler, Jul 12 2018

Formula

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

(The k=0 term is always 0. Sequence lists coefficients of x, x^2, x^3, ... - M. F. Hasler, Jul 12 2018)