OFFSET
1,3
COMMENTS
See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
FORMULA
Conjecture: G.f.: -x*(-1+5*x-20*x^2+30*x^3-25*x^4+8*x^5) / ( (x-1)*(x^2+x-1)^5 ). - R. J. Mathar, May 04 2014
MATHEMATICA
c[n_] := n (n + 1) (n + 2) (n + 3)/24; (* binomial B(n, 4), A000332 *)
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 + 1]
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,
40}]
Table[Coefficient[Part[t, n], x, 0], {n, 1, 40}] (* A192248 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 40}] (* A192249 *)
Table[Coefficient[Part[t, n]/5, x, 1], {n, 1, 40}] (* A192069 *)
(* by Peter J. C. Moses, Jun 20 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 27 2011
STATUS
approved