OFFSET
1,3
COMMENTS
The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + 1 + n*x/f(n-1,x), where f(1,x) = 1.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..5050
EXAMPLE
f(1,x) = 1/1, so that p(1,x) = 1
f(2,x) = (1 + 3 x)/1, so that p(2,x) = 1 + 3 x;
f(3,x) = (1 + 7 x + 3 x^2)/(1 + 3 x), so that p(3,x) = 1 + 7 x + 3 x^2.
First 6 rows of the triangle of coefficients:
1
1 3
1 7 3
1 12 22 3
1 18 69 40 3
1 25 150 241 61 3
MATHEMATICA
PROG
(PARI) rown(n) = if (n==1, 1, x + 1 + n*x/rown(n-1));
tabl(nn) = for (n=1, nn, print(Vecrev(numerator(rown(n))))); \\ Michel Marcus, Oct 30 2014
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 24 2014
STATUS
approved