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A193797
Mirror of the triangle A193796.
2
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.
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 05 2011
STATUS
approved