A193797 Mirror of the triangle A193796.

1, 1, 1, 5, 2, 3, 25, 4, 12, 9, 125, 8, 36, 54, 27, 625, 16, 96, 216, 216, 81, 3125, 32, 240, 720, 1080, 810, 243, 15625, 64, 576, 2160, 4320, 4860, 2916, 729, 78125, 128, 1344, 6048, 15120, 22680, 20412, 10206, 2187, 390625, 256, 3072, 16128, 48384

Offset

0,4

Comments

A193797 is obtained by reversing the rows of the triangle A193796.

Links

Table of n, a(n) for n=0..49.

Example

Write w(n,k) for the triangle at A193796.  The triangle at A193797 is then given by w(n,n-k).
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 = 8; a = 2; 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}]]  (* A193796 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193797 *)

Crossrefs

Cf. A193796.

Sequence in context: A248262 A291690 A073943 * A350518 A214662 A277581

Adjacent sequences: A193794 A193795 A193796 * A193798 A193799 A193800

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 05 2011

Status

approved