|
%I #23 Jul 15 2018 13:30:30
%S 1,1,3,1,9,11,1,21,66,50,1,45,275,500,274,1,93,990,3250,4110,1764,1,
%T 189,3311,17500,38360,37044,13068,1,381,10626,85050,287700,469224,
%U 365904,109584,1,765,33275,388500,1904574,4667544,6037416,3945024,1026576,1,1533,102630,1705250,11651850,40266828,76839840,82188000,46195920,10628640
%N Triangle read by rows: coefficients of harmonic-geometric polynomials.
%H Ayhan Dil and Veli Kurt, <a href="https://www.emis.de/journals/INTEGERS/papers/m38/m38.Abstract.html">Polynomials related to harmonic numbers and evaluation of harmonic number series I</a>, INTEGERS, 12 (2012), #A38.
%F The n-th polynomial is Sum_{k=0..n} Stirling2(n,k)*|Stirling1(k+1,2)|*x^k.
%F (The k=0 term is always 0. Sequence lists coefficients of x, x^2, x^3, ... - _M. F. Hasler_, Jul 12 2018)
%e Triangle begins:
%e 1;
%e 1, 3;
%e 1, 9, 11;
%e 1, 21, 66, 50;
%e 1, 45, 275, 500, 274;
%e 1, 93, 990, 3250, 4110, 1764;
%e 1, 189, 3311, 17500, 38360, 37044, 13068;
%e 1, 381, 10626, 85050, 287700, 469224, 365904, 109584;
%e ...
%o (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
%Y Row sums give A222058. See A222060 for another version (including row & column 0).
%K nonn,tabl
%O 1,3
%A _N. J. A. Sloane_, Feb 08 2013
|
