A193795 Mirror of the triangle A193794.

1, 1, 1, 4, 3, 1, 16, 9, 6, 1, 64, 27, 27, 9, 1, 256, 81, 108, 54, 12, 1, 1024, 243, 405, 270, 90, 15, 1, 4096, 729, 1458, 1215, 540, 135, 18, 1, 16384, 2187, 5103, 5103, 2835, 945, 189, 21, 1, 65536, 6561, 17496, 20412, 13608, 5670, 1512, 252, 24, 1, 262144

Offset

0,4

Comments

A193795 is obtained by reversing the rows of the triangle A193794.

Links

Table of n, a(n) for n=0..55.

Formula

Write w(n,k) for the triangle at A193794. The triangle at A193795 is then given by w(n,n-k).

Example

First six rows:
1
1.....1
4.....3....1
16....9....6....1
64....27...27...9...1
256...81...108..54..12...1

Mathematica

z = 9; a = 3; b = 1;
p[n_, x_] := (a*x + b)^n
q[n_, x_] := 1 + x^n ; q[n_, 0] := q[n, x] /. x -> 0;
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193794 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193795 *)

Crossrefs

Cf. A193794.

Sequence in context: A010305 A308326 A098234 * A181355 A128320 A189507

Adjacent sequences: A193792 A193793 A193794 * A193796 A193797 A193798

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 05 2011

Status

approved