OFFSET
0,2
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..5049
EXAMPLE
f(0,x) = 1/1, so that p(0,x) = 1
f(1,x) = (4 + x)/1, so that p(1,x) = 4 + x;
f(2,x) = (5 + 4 x + x^2)/(1 + x), so that p(2,x) = 5 + 4 x + x^2.
First 6 rows of the triangle of coefficients:
1
4 1
5 4 1
24 11 4 1
35 52 18 4 1
192 123 84 26 4 1
MATHEMATICA
z = 12; f[x_, n_] := x + (n+3)/f[x, n - 1];
f[x_, 0] = 1; t = Table[Factor[f[x, n]], {n, 0, z}];
u = Numerator[t]; TableForm[Rest[Table[CoefficientList[u[[n]], x], {n, 0, z}]]];
Flatten[CoefficientList[u, x]] (* A249057 sequence *)
PROG
(PARI) f(n) = if (n, x + (n + 3)/f(n-1), 1);
row(n) = Vecrev(numerator(f(n)), 0); \\ Michel Marcus, Nov 25 2022
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 20 2014
STATUS
approved