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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. 1
 1, 3, 2, 6, 8, 3, 45, 32, 15, 4, 126, 256, 90, 24, 5, 750, 1536, 885, 192, 35, 6, 2796, 12288, 8010, 2304, 350, 48, 7, 19389, 90112, 85590, 27648, 5005, 576, 63, 8, 75894, 753664, 913140, 374784, 74550, 9600, 882, 80, 9 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..45. Neil J. Calkin, Eunice Y. S. Chan, and Robert M. Corless, Some Facts and Conjectures about Mandelbrot Polynomials, Maple Trans., Vol. 1, No. 1, Article 14037 (July 2021). Michael Larsen, Multiplicative series, modular forms, and Mandelbrot polynomials, in: Mathematics of Computation 90.327 (Sept. 2020), pp. 345-377. Preprint: arXiv:1908.09974 [math.NT], 2019. EXAMPLE Array starts: [1] 1, 2, 3, 4, 5, 6, 7, ... [2] 3, 8, 15, 24, 35, 48, 63, ... [3] 6, 32, 90, 192, 350, 576, 882, ... [4] 45, 256, 885, 2304, 5005, 9600, 16821, ... [5] 126, 1536, 8010, 27648, 74550, 170496, 346626, ... [6] 750, 12288, 85590, 374784, 1229550, 3317760, 7778358, ... [7] 2796, 90112, 913140, 5210112, 21017500, 67239936, 182244132, ... [8] 19389, 753664, 10384845, 75890688, 374119165, 1415184384, 4428038349, ... Seen as a triangle: [1] 1; [2] 3, 2; [3] 6, 8, 3; [4] 45, 32, 15, 4; [5] 126, 256, 90, 24, 5; [6] 750, 1536, 885, 192, 35, 6; [7] 2796, 12288, 8010, 2304, 350, 48, 7; [8] 19389, 90112, 85590, 27648, 5005, 576, 63, 8; [9] 75894, 753664, 913140, 374784, 74550, 9600, 882, 80, 9; MAPLE # Polynomials M are defined in A347928. P := (n, x) -> 2^(2*n-1)*M(n, x): row := (n, len) -> seq(P(n, k), k = 1..len): for n from 1 to 8 do row(n, 8) od; CROSSREFS Cf. A347928, A319539, A088674. Sequence in context: A193998 A209171 A368150 * A160855 A120232 A292961 Adjacent sequences: A348683 A348684 A348685 * A348687 A348688 A348689 KEYWORD nonn,tabl AUTHOR Peter Luschny, Oct 29 2021 STATUS approved

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Last modified June 17 00:51 EDT 2024. Contains 373432 sequences. (Running on oeis4.)