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

1,3

Links

Table of n, a(n) for n=1..55.

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.

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

Example

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;
  ...

Prog

(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

Crossrefs

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

Sequence in context: A225469 A095069 A184061 * A260285 A242499 A354622

Adjacent sequences: A222054 A222055 A222056 * A222058 A222059 A222060

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 08 2013

Status

approved