A348679 - OEIS

%I #6 Oct 29 2021 11:59:30

%S 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,

%T 25,45,63,33,0,1,7,21,245,7,385,231,429,0,0,1,9,45,555,129,819,429,

%U 715,0,0,3,45,55,1155,2695,2387,3465,6435,2431

%N 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.

%H Neil J. Calkin, Eunice Y. S. Chan, and Robert M. Corless, <a href="https://doi.org/10.5206/mt.v1i1.14037">Some Facts and Conjectures about Mandelbrot Polynomials</a>, Maple Trans., Vol. 1, No. 1, Article 14037 (July 2021).

%H Michael Larsen, <a href="https://doi.org/10.1090/mcom/3564">Multiplicative series, modular forms, and Mandelbrot polynomials</a>, in: Mathematics of Computation 90.327 (Sept. 2020), pp. 345-377. Preprint: <a href="https://arxiv.org/abs/1908.09974">arXiv:1908.09974</a> [math.NT], 2019.

%e Triangle read by rows:

%e [0] 0

%e [1] 0, 1

%e [2] 0, 1, 1

%e [3] 0, 0, 1,  1

%e [4] 0, 1, 3,  3,   5

%e [5] 0, 0, 1,  5,   5, 7

%e [6] 0, 0, 3, 13,  21,  35,  21

%e [7] 0, 0, 0,  5,  25,  45,  63,  33

%e [8] 0, 1, 7, 21, 245,   7, 385, 231, 429

%e [9] 0, 0, 1,  9,  45, 555, 129, 819, 429, 715

%p # Polynomials M are defined in A347928.

%p T := (n, k) -> numer(coeff(M(n, x), x, k)):

%p for n from 0 to 9 do seq(T(n, k), k = 0..n) od;

%Y T(n, n) = A098597(n).

%Y Cf. A348678 (denominators), A347928.

%K nonn,tabl,frac

%O 0,13

%A _Peter Luschny_, Oct 29 2021