A192248 0-sequence of reduction of binomial coefficient sequence B(n,4)=A000332 by x^2 -> x+1.

1, 1, 16, 51, 191, 569, 1619, 4259, 10694, 25709, 59743, 134818, 296798, 639518, 1352498, 2813750, 5769200, 11676395, 23358450, 46239770, 90667076, 176244326, 339887026, 650715076, 1237467151, 2338753519, 4394813644, 8214444389

Offset

1,3

Comments

See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".

Links

Table of n, a(n) for n=1..28.

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

Cf. A192232, A192249, A192069.

Sequence in context: A204962 A080860 A204716 * A363350 A297640 A236523

Adjacent sequences: A192245 A192246 A192247 * A192249 A192250 A192251

Keyword

nonn

Author

Clark Kimberling, Jun 27 2011

Status

approved