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%I #9 Oct 29 2021 17:44:23
%S 1,1,2,1,4,8,1,1,8,16,1,8,32,32,128,1,1,16,64,64,256,1,1,32,128,256,
%T 512,1024,1,1,1,64,256,512,1024,2048,1,16,128,256,2048,64,4096,4096,
%U 32768,1,1,32,256,512,4096,1024,8192,8192,65536
%N Triangle read by rows, T(n, k) = denominator([x^k] M(n, x)) where M(n,x) are the 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 Triangle starts:
%e [0] 1
%e [1] 1, 2
%e [2] 1, 4, 8
%e [3] 1, 1, 8, 16
%e [4] 1, 8, 32, 32, 128
%e [5] 1, 1, 16, 64, 64, 256
%e [6] 1, 1, 32, 128, 256, 512, 1024
%e [7] 1, 1, 1, 64, 256, 512, 1024, 2048
%e [8] 1, 16, 128, 256, 2048, 64, 4096, 4096, 32768
%e [9] 1, 1, 32, 256, 512, 4096, 1024, 8192, 8192, 65536
%p # Polynomials M are defined in A347928.
%p T := (n, k) -> denom(coeff(M(n, x), x, k)):
%p for n from 0 to 9 do seq(T(n, k), k = 0..n) od;
%Y T(n, n) = A046161(n).
%Y Cf. A348679 (numerators), A347928, A088802 & A123854 (central elements).
%K nonn,tabl,frac
%O 0,3
%A _Peter Luschny_, Oct 29 2021
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