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A137423
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Triangular sequence based on the combination of Pascal coefficients summed with Chebyshev coefficients of the first kind T(x,n)/ A053120: q(x,n)=t(x,n)+(x+1)^n.
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0
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2, 1, 2, 0, 2, 3, 1, 0, 3, 5, 2, 4, -2, 4, 9, 1, 10, 10, -10, 5, 17, 0, 6, 33, 20, -33, 6, 33, 1, 0, 21, 91, 35, -91, 7, 65, 2, 8, -4, 56, 230, 56, -228, 8, 129, 1, 18, 36, -36, 126, 558, 84, -540, 9, 257, 0, 10, 95, 120, -190, 252, 1330, 120, -1235, 10, 513
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are:
A000051:
{2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025}
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FORMULA
| q(x,0)=2;q(x,2)=x+1+T(x,1); q(x,n)=t(x,n)+(x+1)^n
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EXAMPLE
| {2},
{1, 2},
{0, 2, 3},
{1, 0, 3, 5},
{2, 4, -2, 4, 9},
{1, 10, 10, -10, 5, 17},
{0, 6, 33, 20, -33, 6, 33},
{1, 0, 21, 91, 35, -91, 7, 65},
{2, 8, -4, 56, 230, 56, -228, 8, 129},
{1, 18, 36, -36, 126, 558, 84, -540, 9, 257},
{0, 10, 95, 120, -190, 252, 1330, 120, -1235, 10, 513}
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MATHEMATICA
| (* Chebyshev A053120 polynomials*) (* addition of coefficients of Polynomials*) Q[x, 0] = 2; Q[x, 1] = x + 1 + ChebyshevT[1, x]; Q[x_, n_] := (x + 1)^n + ChebyshevT[n, x]; Table[ExpandAll[Q[x, n]], {n, 0, 10}]; a0 = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a0]
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CROSSREFS
| Cf. A053120.
Sequence in context: A093321 A046144 A144736 * A127471 A071485 A127969
Adjacent sequences: A137420 A137421 A137422 * A137424 A137425 A137426
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KEYWORD
| tabl,uned,sign
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AUTHOR
| Roger L. Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Apr 16 2008
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