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A348678 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.

%I A348678 #9 Oct 29 2021 17:44:23
%S A348678 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 A348678 512,1024,1,1,1,64,256,512,1024,2048,1,16,128,256,2048,64,4096,4096,
%U A348678 32768,1,1,32,256,512,4096,1024,8192,8192,65536
%N A348678 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 A348678 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 A348678 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 A348678 Triangle starts:
%e A348678 [0] 1
%e A348678 [1] 1,  2
%e A348678 [2] 1,  4,   8
%e A348678 [3] 1,  1,   8,  16
%e A348678 [4] 1,  8,  32,  32,  128
%e A348678 [5] 1,  1,  16,  64,   64,  256
%e A348678 [6] 1,  1,  32, 128,  256,  512, 1024
%e A348678 [7] 1,  1,   1,  64,  256,  512, 1024, 2048
%e A348678 [8] 1, 16, 128, 256, 2048,   64, 4096, 4096, 32768
%e A348678 [9] 1,  1,  32, 256,  512, 4096, 1024, 8192,  8192, 65536
%p A348678 # Polynomials M are defined in A347928.
%p A348678 T := (n, k) -> denom(coeff(M(n, x), x, k)):
%p A348678 for n from 0 to 9 do seq(T(n, k), k = 0..n) od;
%Y A348678 T(n, n) = A046161(n).
%Y A348678 Cf. A348679 (numerators), A347928, A088802 & A123854 (central elements).
%K A348678 nonn,tabl,frac
%O A348678 0,3
%A A348678 _Peter Luschny_, Oct 29 2021