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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.
2
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, 512, 1024, 1, 1, 1, 64, 256, 512, 1024, 2048, 1, 16, 128, 256, 2048, 64, 4096, 4096, 32768, 1, 1, 32, 256, 512, 4096, 1024, 8192, 8192, 65536
OFFSET
0,3
LINKS
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
Triangle starts:
[0] 1
[1] 1, 2
[2] 1, 4, 8
[3] 1, 1, 8, 16
[4] 1, 8, 32, 32, 128
[5] 1, 1, 16, 64, 64, 256
[6] 1, 1, 32, 128, 256, 512, 1024
[7] 1, 1, 1, 64, 256, 512, 1024, 2048
[8] 1, 16, 128, 256, 2048, 64, 4096, 4096, 32768
[9] 1, 1, 32, 256, 512, 4096, 1024, 8192, 8192, 65536
MAPLE
# Polynomials M are defined in A347928.
T := (n, k) -> denom(coeff(M(n, x), x, k)):
for n from 0 to 9 do seq(T(n, k), k = 0..n) od;
CROSSREFS
T(n, n) = A046161(n).
Cf. A348679 (numerators), A347928, A088802 & A123854 (central elements).
Sequence in context: A001933 A373671 A038557 * A011234 A208917 A161381
KEYWORD
nonn,tabl,frac
AUTHOR
Peter Luschny, Oct 29 2021
STATUS
approved