A348679 Triangle read by rows, T(n, k) = numerator([x^k] M(n, x)) where M(n,x) are the Mandelbrot-Larsen polynomials defined in A347928.

0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 3, 3, 5, 0, 0, 1, 5, 5, 7, 0, 0, 3, 13, 21, 35, 21, 0, 0, 0, 5, 25, 45, 63, 33, 0, 1, 7, 21, 245, 7, 385, 231, 429, 0, 0, 1, 9, 45, 555, 129, 819, 429, 715, 0, 0, 3, 45, 55, 1155, 2695, 2387, 3465, 6435, 2431

Offset

0,13

Links

Table of n, a(n) for n=0..65.

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 read by rows:
[0] 0
[1] 0, 1
[2] 0, 1, 1
[3] 0, 0, 1,  1
[4] 0, 1, 3,  3,   5
[5] 0, 0, 1,  5,   5, 7
[6] 0, 0, 3, 13,  21,  35,  21
[7] 0, 0, 0,  5,  25,  45,  63,  33
[8] 0, 1, 7, 21, 245,   7, 385, 231, 429
[9] 0, 0, 1,  9,  45, 555, 129, 819, 429, 715

Maple

# Polynomials M are defined in A347928.
T := (n, k) -> numer(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) = A098597(n).

Cf. A348678 (denominators), A347928.

Sequence in context: A300369 A304296 A076183 * A011445 A197137 A133456

Adjacent sequences: A348676 A348677 A348678 * A348680 A348681 A348682

Keyword

nonn,tabl,frac

Author

Peter Luschny, Oct 29 2021

Status

approved