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A222057 Triangle read by rows: coefficients of harmonic-geometric polynomials. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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 A173020

Adjacent sequences:  A222054 A222055 A222056 * A222058 A222059 A222060

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 08 2013

STATUS

approved

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Last modified May 27 02:54 EDT 2019. Contains 323597 sequences. (Running on oeis4.)