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%I #10 Oct 29 2021 17:15:56
%S 1,3,2,6,8,3,45,32,15,4,126,256,90,24,5,750,1536,885,192,35,6,2796,
%T 12288,8010,2304,350,48,7,19389,90112,85590,27648,5005,576,63,8,75894,
%U 753664,913140,374784,74550,9600,882,80,9
%N Array read by ascending antidiagonals: T(n, k) = P(n, k) where P(n, x) are the scaled Mandelbrot-Larsen polynomials defined in A347928.
%H Neil J. Calkin, Eunice Y. S. Chan, and Robert M. Corless, <a href="https://doi.org/10.5206/mt.v1i1.14037">Some Facts and Conjectures about Mandelbrot Polynomials</a>, Maple Trans., Vol. 1, No. 1, Article 14037 (July 2021).
%H Michael Larsen, <a href="https://doi.org/10.1090/mcom/3564">Multiplicative series, modular forms, and Mandelbrot polynomials</a>, in: Mathematics of Computation 90.327 (Sept. 2020), pp. 345-377. Preprint: <a href="https://arxiv.org/abs/1908.09974">arXiv:1908.09974</a> [math.NT], 2019.
%e Array starts:
%e [1] 1, 2, 3, 4, 5, 6, 7, ...
%e [2] 3, 8, 15, 24, 35, 48, 63, ...
%e [3] 6, 32, 90, 192, 350, 576, 882, ...
%e [4] 45, 256, 885, 2304, 5005, 9600, 16821, ...
%e [5] 126, 1536, 8010, 27648, 74550, 170496, 346626, ...
%e [6] 750, 12288, 85590, 374784, 1229550, 3317760, 7778358, ...
%e [7] 2796, 90112, 913140, 5210112, 21017500, 67239936, 182244132, ...
%e [8] 19389, 753664, 10384845, 75890688, 374119165, 1415184384, 4428038349, ...
%e Seen as a triangle:
%e [1] 1;
%e [2] 3, 2;
%e [3] 6, 8, 3;
%e [4] 45, 32, 15, 4;
%e [5] 126, 256, 90, 24, 5;
%e [6] 750, 1536, 885, 192, 35, 6;
%e [7] 2796, 12288, 8010, 2304, 350, 48, 7;
%e [8] 19389, 90112, 85590, 27648, 5005, 576, 63, 8;
%e [9] 75894, 753664, 913140, 374784, 74550, 9600, 882, 80, 9;
%p # Polynomials M are defined in A347928.
%p P := (n, x) -> 2^(2*n-1)*M(n, x):
%p row := (n, len) -> seq(P(n, k), k = 1..len):
%p for n from 1 to 8 do row(n, 8) od;
%Y Cf. A347928, A319539, A088674.
%K nonn,tabl
%O 1,2
%A _Peter Luschny_, Oct 29 2021