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A193795 Mirror of the triangle A193794. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A112493 A010305 A098234 * A181355 A128320 A189507

Adjacent sequences:  A193792 A193793 A193794 * A193796 A193797 A193798

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 05 2011

STATUS

approved

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Last modified July 23 22:18 EDT 2019. Contains 325269 sequences. (Running on oeis4.)