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A193792
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Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(x+3)^n and q(n,x)=1+x^n.
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2
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1, 1, 1, 3, 1, 4, 9, 6, 1, 16, 27, 27, 9, 1, 64, 81, 108, 54, 12, 1, 256, 243, 405, 270, 90, 15, 1, 1024, 729, 1458, 1215, 540, 135, 18, 1, 4096, 2187, 5103, 5103, 2835, 945, 189, 21, 1, 16384, 6561, 17496, 20412, 13608, 5670, 1512, 252, 24, 1, 65536
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OFFSET
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0,4
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COMMENTS
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See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
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LINKS
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EXAMPLE
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First six rows:
1
1....1
3....1....4
9....6....1....16
27...27...9....1...64
81...108..54...12..1...256
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MATHEMATICA
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z = 8; a = 1; 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}]] (* A193792 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193793 *)
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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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