OFFSET
0,2
COMMENTS
For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232.
FORMULA
Conjecture: a(n) +(-4*n+1)*a(n-1) +(4*n^2-6*n+1)*a(n-2)=0. - R. J. Mathar, May 08 2014
EXAMPLE
MATHEMATICA
q = x^2; s = x + 1; z = 26;
p[0, x] := 1;
p[n_, x_] := (x + 2 n)*p[n - 1, x];
Table[Expand[p[n, x]], {n, 0, 7}]
reduce[{p1_, q_, s_, x_}] :=
FixedPoint[(s PolynomialQuotient @@ #1 +
PolynomialRemainder @@ #1 &)[{#1, q, x}] &, p1]
t = Table[reduce[{p[n, x], q, s, x}], {n, 0, z}];
u1 = Table[Coefficient[Part[t, n], x, 0], {n, 1, z}]
(* A192939 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]
(* A192940 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 13 2011
STATUS
approved