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A123019
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Triangular array from a Bezier transform of the Morgan-Voyce Polynomials with recursion:F(n+1,x)=xF(n,x)+F(n-1,x):triangular T(n, k) := binomial[n + k, n - k].
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0
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1, 1, 1, 1, -1, 1, 3, -4, 1, 1, 6, -9, 3, 1, 10, -15, 3, 3, -1, 1, 15, -20, -6, 18, -8, 1, 1, 21, -21, -35, 60, -30, 5, 1, 28, -14, -98, 145, -70, 5, 5, -1, 1, 36, 6, -210, 279, -100, -45, 45, -12, 1, 1, 45, 45, -384, 441, -21, -280, 210, -63, 7
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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REFERENCES
| Eric Weisstein's World of Mathematics, "Morgan-Voyce Polynomials." http://mathworld.wolfram.com/Morgan-VoycePolynomials.html
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FORMULA
| T(n, k) := binomial[n + k, n - k] (* Bezier transform:*) T'(n,k)=T(n, k)*p^k*(1 - p)^(n - k)
G.f.: x*(1+x*(y-1))/(1+(y-2)*x+(y-1)^2*x^2). [From Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 14 2009]
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EXAMPLE
| 1
1
1, 1, -1
1, 3,-4, 1
1, 6,-9, 3
1, 10,-15, 3, 3,-1
1, 15, -20, -6, 18,-8, 1
1, 21, -21, -35, 60, -30, 5
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MATHEMATICA
| T[n_, k_] := Binomial[n + k, n - k]; a = Table[CoefficientList[Sum[T[n, k]*p^k*(1 - p)^(n - k), {k, 0, n}], p], {n, 0, 10}]; Flatten[a]
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CROSSREFS
| Cf. A085478.
Sequence in context: A073366 A001086 A105283 * A204999 A085710 A106650
Adjacent sequences: A123016 A123017 A123018 * A123020 A123021 A123022
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KEYWORD
| sign,uned,tabl
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AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 24 2006
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