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A109576
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E.g.f.: x/(1+3x-4x^3)=x/[1-T(3,x)], where T(3,x) is a Chebyshev polynomial.
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0
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0, 1, -6, 54, -552, 6840, -97200, 1577520, -28667520, 578067840, -12798777600, 308836281600, -8065907942400, 226719600307200, -6824229456844800, 219010610827008000, -7465397891567616000, 269363867734241280000, -10256545055212904448000
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OFFSET
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0,3
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COMMENTS
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"Bernoulli numbers" for x/[1-T(3,x)].
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LINKS
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FORMULA
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D-finite with recurrence a(n) +(n+4)*a(n-1) -2*n*(n-1)*a(n-2) -4*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Aug 20 2021
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MAPLE
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G:=x/(1+3*x-4*x^3): Gser:=series(G, x=0, 23): 0, seq(n!*coeff(Gser, x^n), n=1..20); # yields the signed sequence
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MATHEMATICA
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g[x_] = x/(-1 + ChebyshevT[3, x]) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[h[x, n], {n, 0, 50}]; b = a[0]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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