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A193822
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Mirror of the triangle A193821.
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4
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1, 1, 1, 3, 3, 2, 9, 9, 8, 4, 27, 27, 26, 20, 8, 81, 81, 80, 72, 48, 16, 243, 243, 242, 232, 192, 112, 32, 729, 729, 728, 716, 656, 496, 256, 64, 2187, 2187, 2186, 2172, 2088, 1808, 1248, 576, 128, 6561, 6561, 6560, 6544, 6432, 5984, 4864, 3072, 1280, 256
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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Write w(n,k) for the triangle at A193821. The triangle at A193822 is then given by w(n,n-k).
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EXAMPLE
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First six rows:
1
1....1
3....3....2
9....9....8.....4
27...27...26....20...8
81...81...80....72...48...16
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MATHEMATICA
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p[n_, x_] := (a*x + b)^n
q[0, x_] := 1
q[n_, x_] := x*q[n - 1, x] + 1; 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}]] (* A193821 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193822 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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