OFFSET
0,3
COMMENTS
The polynomial p(n,x) is given by p(n,x) = (x + 1)*p(n-1,x) + 2x, where p(0,x) = 1.
LINKS
Clark Kimberling, Rows 0..100, flattened
EXAMPLE
f(0,x) = 1/1, so that p(0,x) = 1
f(1,x) = (1 + 3 x)/1, so that p(1,x) = 1 + 3 x;
f(2,x) = (1 + 6 x + 3 x^2)/(1 + 3 x), so that p(2,x) = 1 + 6 x + 3 x^2.
First 6 rows of the triangle of coefficients:
1
1 3
1 6 3
1 9 15 3
1 12 36 24 3
1 15 66 90 33 3
MATHEMATICA
PROG
(PARI) rown(n) = if (n==0, 1, x + 1 + 2*x/rown(n-1));
tabl(nn) = for (n=0, nn, print(Vecrev(numerator(rown(n))))); \\ Michel Marcus, Oct 28 2014
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 24 2014
STATUS
approved