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A193972
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Mirror of the triangle A193971.
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2
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2, 5, 3, 9, 11, 4, 14, 26, 19, 5, 20, 50, 55, 29, 6, 27, 85, 125, 99, 41, 7, 35, 133, 245, 259, 161, 55, 8, 44, 196, 434, 574, 476, 244, 71, 9, 54, 276, 714, 1134, 1176, 804, 351, 89, 10, 65, 375, 1110, 2058, 2562, 2190, 1275, 485, 109, 11, 77, 495, 1650
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OFFSET
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0,1
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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 A193971. The triangle at A193972 is then given by w(n,n-k).
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EXAMPLE
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First six rows:
2
5....3
9....11...4
14...26...19....5
20...50...55....29...6
27...85...125...99...41...7
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MATHEMATICA
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z = 11;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
q[n_, x_] := (x + 1)^n
p1[n_, k_] := Coefficient[p[n, x], x^k];
p1[n_, 0] := p[n, x] /. x -> 0;
d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
h[n_] := CoefficientList[d[n, x], {x}]
TableForm[Table[Reverse[h[n]], {n, 0, z}]]
Flatten[Table[Reverse[h[n]], {n, -1, z}]] (* A193971 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]] (* A193972 *)
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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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