A193793 Mirror of the triangle A193792.

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

Offset

0,4

Comments

A193793 is obtained by reversing the rows of the triangle A193792.

Links

Table of n, a(n) for n=0..54.

Formula

Write w(n,k) for the triangle at A193792. The triangle at A193793 is then given by w(n,n-k).

Example

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

Mathematica

z = 8; a = 1; b = 3;
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}]]  (* A193792 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193793 *)

Crossrefs

Cf. A193792.

Sequence in context: A156224 A162516 A336693 * A301510 A085471 A064221

Adjacent sequences: A193790 A193791 A193792 * A193794 A193795 A193796

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 05 2011

Status

approved