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A193861
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Mirror of the triangle A193860.
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3
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1, 5, 1, 19, 7, 1, 65, 33, 9, 1, 211, 131, 51, 11, 1, 665, 473, 233, 73, 13, 1, 2059, 1611, 939, 379, 99, 15, 1, 6305, 5281, 3489, 1697, 577, 129, 17, 1, 19171, 16867, 12259, 6883, 2851, 835, 163, 19, 1, 58025, 52905, 41385, 26025, 12585, 4521, 1161
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OFFSET
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0,2
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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 A193860. The triangle at A193861 is then given by w(n,n-k).
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EXAMPLE
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First six rows:
1
5.....1
19....7.....1
65....33....9.....1
211...131...51....11...1
665...473...233...73...13...1
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MATHEMATICA
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z = 10;
p[n_, x_] := (2 x + 1)^n;
q[0, x_] := 1; q[n_, x_] := x*q[n - 1, x] + 1;
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}]] (* A193860 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]] (* A193861 *)
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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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