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A156857
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Expansion of (1+2*x)/(1+x+4*x^2)^2.
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1
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1, 0, -9, 10, 45, -108, -125, 702, -135, -3320, 4239, 11250, -31931, -18180, 165915, -92762, -651375, 1101168, 1747495, -6710310, -694179, 30182500, -28394829, -101934450, 229069225, 203510232, -1198850625, 364506562, 4767453045
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1 +2*x)/(1 +2*x +9*x^2 +8*x^3 +16*x^4).
a(n) = (-2)*Sum_{j=0..n} ChebyshevU(n-j, 1/4)*(ChebyshevU(j, 1/4) - ChebyshevU(j-1, 1/4)). - G. C. Greubel, Jan 28 2022
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MATHEMATICA
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LinearRecurrence[{-2, -9, -8, -16}, {1, 0, -9, 10}, 41] (* or *)
A156857[n_]:= (-2)^n*Sum[ChebyshevU[n-j, 1/4]*(ChebyshevU[j, 1/4] - ChebyshevU[j-1, 1/4]), {j, 0, n}];
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PROG
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(Magma) I:=[1, 0, -9, 10]; [n le 4 select I[n] else (-1)*(2*Self(n-1) +9*Self(n-2) +8*Self(n-3) +16*Self(n-4)): n in [1..41]]; // G. C. Greubel, Jan 28 2022
(Sage)
def A156857(n): return (-2)^n*sum( chebyshev_U(n-j, 1/4)*(chebyshev_U(j, 1/4) - chebyshev_U(j-1, 1/4)) for j in (0..n))
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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