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A193789
Mirror of the triangle A193788.
3
1, 1, 1, 3, 1, 2, 9, 1, 4, 4, 27, 1, 6, 12, 8, 81, 1, 8, 24, 32, 16, 243, 1, 10, 40, 80, 80, 32, 729, 1, 12, 60, 160, 240, 192, 64, 2187, 1, 14, 84, 280, 560, 672, 448, 128, 6561, 1, 16, 112, 448, 1120, 1792, 1792, 1024, 256, 19683, 1, 18, 144, 672, 2016, 4032
OFFSET
0,4
COMMENTS
A193789 is obtained by reversing the rows of the triangle A193788.
FORMULA
Write w(n,k) for the triangle at A193788. The triangle at A193789 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....1
3....1....2
9....1....4....4
27...1....6....12...8
81...1....8....24...32...16
MATHEMATICA
z = 10; a = 1; b = 2;
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}]] (* A193788 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193789 *)
CROSSREFS
Sequence in context: A086961 A204003 A085194 * A152252 A152229 A238388
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 05 2011
STATUS
approved