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A348686 Array read by ascending antidiagonals: T(n, k) = P(n, k) where P(n, x) are the scaled Mandelbrot-Larsen polynomials defined in A347928.

%I A348686 #10 Oct 29 2021 17:15:56
%S A348686 1,3,2,6,8,3,45,32,15,4,126,256,90,24,5,750,1536,885,192,35,6,2796,
%T A348686 12288,8010,2304,350,48,7,19389,90112,85590,27648,5005,576,63,8,75894,
%U A348686 753664,913140,374784,74550,9600,882,80,9
%N A348686 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 A348686 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 A348686 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 A348686 Array starts:
%e A348686 [1] 1,     2,      3,        4,        5,         6,          7, ...
%e A348686 [2] 3,     8,      15,       24,       35,        48,         63, ...
%e A348686 [3] 6,     32,     90,       192,      350,       576,        882, ...
%e A348686 [4] 45,    256,    885,      2304,     5005,      9600,       16821, ...
%e A348686 [5] 126,   1536,   8010,     27648,    74550,     170496,     346626, ...
%e A348686 [6] 750,   12288,  85590,    374784,   1229550,   3317760,    7778358, ...
%e A348686 [7] 2796,  90112,  913140,   5210112,  21017500,  67239936,   182244132, ...
%e A348686 [8] 19389, 753664, 10384845, 75890688, 374119165, 1415184384, 4428038349, ...
%e A348686 Seen as a triangle:
%e A348686 [1] 1;
%e A348686 [2] 3,     2;
%e A348686 [3] 6,     8,      3;
%e A348686 [4] 45,    32,     15,     4;
%e A348686 [5] 126,   256,    90,     24,     5;
%e A348686 [6] 750,   1536,   885,    192,    35,    6;
%e A348686 [7] 2796,  12288,  8010,   2304,   350,   48,   7;
%e A348686 [8] 19389, 90112,  85590,  27648,  5005,  576,  63,  8;
%e A348686 [9] 75894, 753664, 913140, 374784, 74550, 9600, 882, 80, 9;
%p A348686 # Polynomials M are defined in A347928.
%p A348686 P := (n, x) -> 2^(2*n-1)*M(n, x):
%p A348686 row := (n, len) -> seq(P(n, k), k = 1..len):
%p A348686 for n from 1 to 8 do row(n, 8) od;
%Y A348686 Cf. A347928, A319539, A088674.
%K A348686 nonn,tabl
%O A348686 1,2
%A A348686 _Peter Luschny_, Oct 29 2021