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A193819
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Mirror of the triangle A193818.
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2
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1, 1, 2, 2, 6, 4, 3, 12, 16, 8, 4, 20, 40, 40, 16, 5, 30, 80, 120, 96, 32, 6, 42, 140, 280, 336, 224, 64, 7, 56, 224, 560, 896, 896, 512, 128, 8, 72, 336, 1008, 2016, 2688, 2304, 1152, 256, 9, 90, 480, 1680, 4032, 6720, 7680, 5760, 2560, 512, 10, 110, 660
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refs;
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history;
text;
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OFFSET
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0,3
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COMMENTS
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A193819 is obtained by reversing the rows of the triangle A193818.
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LINKS
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Table of n, a(n) for n=0..57.
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FORMULA
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Write w(n,k) for the triangle at A193818. The triangle at A193819 is then given by w(n,n-k).
Triangle T(n,k), read by rows, given by (1,1,-1,1,0,0,0,0,0,0,0,...) DELTA (2,0,-2,2,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - From Philippe Deléham, Oct 05 2011.
T(n,k)=A153861(n,k)*2^k. - From Philippe Deléham, Oct 09 2011.
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EXAMPLE
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First six rows:
1
1....2
2....6....4
3....12...16....8
4....20...40....40...16
5....30...80....120..96...32
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MATHEMATICA
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z = 10; c = 2; d = 1;
p[0, x_] := 1
p[n_, x_] := x*p[n - 1, x] + 1; p[n_, 0] := p[n, x] /. x -> 0;
q[n_, x_] := (c*x + d)^n
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}]] (* A193818 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193819 *)
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CROSSREFS
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Cf. A084938, A193722, A193818.
Sequence in context: A137316 A064851 A134458 * A182786 A009279 A059943
Adjacent sequences: A193816 A193817 A193818 * A193820 A193821 A193822
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Aug 06 2011
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STATUS
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approved
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