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A193799
Mirror of the triangle A193798.
2
1, 1, 1, 5, 3, 2, 25, 9, 12, 4, 125, 27, 54, 36, 8, 625, 81, 216, 216, 96, 16, 3125, 243, 810, 1080, 720, 240, 32, 15625, 729, 2916, 4860, 4320, 2160, 576, 64, 78125, 2187, 10206, 20412, 22680, 15120, 6048, 1344, 128, 390625, 6561, 34992, 81648, 108864
OFFSET
0,4
COMMENTS
A193799 is obtained by reversing the rows of the triangle A193798.
FORMULA
Write w(n,k) for the triangle at A193798. The triangle at A193799 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1.....1
5.....3....2
25....9....12....4
125...27...54....36...8
625...81...216...216..96..16
MATHEMATICA
z = 8; a = 3; 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}]] (* A193798 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193799 *)
CROSSREFS
Cf. A193798.
Sequence in context: A322289 A259228 A241182 * A262225 A330092 A064812
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 05 2011
STATUS
approved