cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A222057 #23 Jul 15 2018 13:30:30
%S A222057 1,1,3,1,9,11,1,21,66,50,1,45,275,500,274,1,93,990,3250,4110,1764,1,
%T A222057 189,3311,17500,38360,37044,13068,1,381,10626,85050,287700,469224,
%U A222057 365904,109584,1,765,33275,388500,1904574,4667544,6037416,3945024,1026576,1,1533,102630,1705250,11651850,40266828,76839840,82188000,46195920,10628640
%N A222057 Triangle read by rows: coefficients of harmonic-geometric polynomials.
%H A222057 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 A222057 The n-th polynomial is Sum_{k=0..n} Stirling2(n,k)*|Stirling1(k+1,2)|*x^k.
%F A222057 (The k=0 term is always 0. Sequence lists coefficients of x, x^2, x^3, ... - _M. F. Hasler_, Jul 12 2018)
%e A222057 Triangle begins:
%e A222057   1;
%e A222057   1,   3;
%e A222057   1,   9,    11;
%e A222057   1,  21,    66,    50;
%e A222057   1,  45,   275,   500,    274;
%e A222057   1,  93,   990,  3250,   4110,   1764;
%e A222057   1, 189,  3311, 17500,  38360,  37044,  13068;
%e A222057   1, 381, 10626, 85050, 287700, 469224, 365904, 109584;
%e A222057   ...
%o A222057 (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 A222057 Row sums give A222058. See A222060 for another version (including row & column 0).
%K A222057 nonn,tabl
%O A222057 1,3
%A A222057 _N. J. A. Sloane_, Feb 08 2013