OFFSET
0,6
COMMENTS
FORMULA
The row polynomials satisfy the second order recurrence equation R(n,x) = (n*x+1)*R(n-1,x-1) - (n-1)*(x-1)*R(n-2,x-2), with the initial conditions R(0,x) = 1 and R(1,x) = 1+x. - Peter Bala, Aug 19 2013
EXAMPLE
1
x + 1
2*x^2 + 1
6*x^3 - 12*x^2 + 9*x + 1
24*x^4 - 120*x^3 + 204*x^2 - 104*x + 1
120*x^5 - 1080*x^4 + 3540*x^3 - 4840*x^2 + 2265*x + 1
MAPLE
# Define row polynomials R(n, x) recursively:
R := proc(n, x) option remember; if n = 0 then 1 elif n = 1 then 1+x
else (n*x+1)*procname(n-1, x-1) - (n-1)*(x-1)*procname(n-2, x-2) fi end:
Trow := n -> PolynomialTools:-CoefficientList(R(n, x), x);
seq(Trow(n), n = 0..10); # Peter Bala, Aug 19 2013
MATHEMATICA
R[n_, x_] := R[n, x] = (n x + 1) R[n-1, x-1] - (n-1) (x-1) R[n-2, x-2]; R[0, _] = 1; R[1, x_] = 1 + x;
Table[CoefficientList[R[n, x], x], {n, 0, 8}] // Flatten (* Jean-François Alcover, Nov 13 2019 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Ralf Stephan, Oct 28 2004
STATUS
approved