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

0,3

Links

Table of n, a(n) for n=0..54.

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: A146004 A001933 A038557 * A011234 A208917 A161381

Adjacent sequences: A348675 A348676 A348677 * A348679 A348680 A348681

Keyword

nonn,tabl,frac

Author

Peter Luschny, Oct 29 2021

Status

approved