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A209404
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Negated coefficients of Chebyshev T polynomials: a(n) = -A053120(n+14, n), n >= 0.
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3
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1, 15, 128, 816, 4320, 20064, 84480, 329472, 1208064, 4209920, 14057472, 45260800, 141213696, 428654592, 1270087680, 3683254272, 10478223360, 29297934336, 80648077312, 218864025600, 586290298880, 1551944908800, 4063273943040
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OFFSET
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0,2
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COMMENTS
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The MAGMA program provided calculates the coefficients of order one Chebyshev polynomials, for any arbitrary level. For example, setting Rn to 0 produces A001792, 1 produces A001793, 2 produces A001794, 3 produces A006974, 4 produces A006975, and 5 produces A006976. This sequence is produced with an Rn of 6.
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LINKS
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FORMULA
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a(n) = 2^(n-1)*binomial(n+6, 6)*(n+14)/7 = -A053120(n+14, n), n >= 0. [See a comment in A053120 on subdiagonal sequences. - Wolfdieter Lang, Jan 03 2020]
E.g.f.: (1/315)*exp(2*x)*(315 + 4095*x + 11340*x^2 + 11550*x^3 + 5250*x^4 + 1134*x^5 + 112*x^6 + 4*x^7). - Stefano Spezia, Oct 17 2019
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MAPLE
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seq(2^(n-1)*(n+14)*binomial(n+6, 6)/7, n=0..30); # G. C. Greubel, Oct 18 2019
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MATHEMATICA
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CoefficientList[Series[(1-x)/(1-2*x)^8, {x, 0, 30}], x] (* or *) Table[2^(n-1)*Binomial[n+6, 6]*(n+14)/7, {n, 0, 30}] (* G. C. Greubel, Jan 03 2018 *)
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PROG
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(Magma) Rn:=6; [2^(n-1)/(Rn+1)*Binomial(n+Rn, Rn)*(n+(Rn+1)*2) : n in [0..22]];
(PARI) for(n=0, 30, print1(2^(n-1)*binomial(n+6, 6)*(n+14)/7, ", ")) \\ G. C. Greubel, Jan 03 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 23); Coefficients(R!( (1-x)/(1-2*x)^8 )); // Marius A. Burtea, Oct 17 2019
(GAP) List([0..30], n-> 2^(n-1)*(n+14)*Binomial(n+6, 6)/7); # G. C. Greubel, Oct 18 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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