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.

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

Author

Peter Luschny, Oct 29 2021

Keywords

• nonn
• tabl
• frac

Examples

			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
		

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.

Crossrefs

T(n, n) = A046161(n).

Cf. A348679 (numerators), A347928, A088802 & A123854 (central elements).

Programs

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;