OFFSET
0,3
COMMENTS
FORMULA
Conjecture: a(n) +(-n-1)*a(n-1) -n*(n-2)*a(n-2) +n*(n-1)*a(n-3)=0. - R. J. Mathar, May 04 2014
Conjecture: a(n) = Sum_{k=0..n} A052554(k). - Sean A. Irvine, Jul 14 2022
EXAMPLE
MATHEMATICA
c[n_] := n!; (* A000142 *)
Table[c[n], {n, 1, 15}]
q[x_] := x + 1;
p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n]
reductionRules = {x^y_?EvenQ -> q[x]^(y/2), x^y_?OddQ -> x q[x]^((y - 1)/2)};
t = Table[Last[Most[FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0, 50}]
Table[Coefficient[Part[t, n], x, 0], {n, 1, 50}] (* A192252 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 50}] (* A192253 *)
Table[Coefficient[(-7 + Part[t, n])/10, x, 0], {n, 1, 30}]
(* Peter J. C. Moses, Jun 20 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 27 2011
STATUS
approved