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A126984
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Expansion of 1/(1+2*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
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9
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1, -2, 2, -4, 2, -12, -12, -72, -190, -700, -2308, -8120, -28364, -100856, -360792, -1301904, -4727358, -17268636, -63405012, -233885784, -866327748, -3220976616, -12016209192, -44966763504, -168750724428, -634935132312, -2394717424552, -9051945482032
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OFFSET
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0,2
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COMMENTS
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Hankel transform is (-2)^n.
Hankel transform omitting first term is (-2)^n omitting first term. Hankel transform omitting first two terms is 2*(-1)^n*A014480(n). - Michael Somos, May 16 2022
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} A039599(n,k)*(-3)^k.
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MAPLE
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c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+2*x*c), x=0, 32): seq(coeff(ser, x, n), n=0..30); # Emeric Deutsch, Mar 24 2007
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MATHEMATICA
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CoefficientList[Series[1/(2-Sqrt[1-4*x]), {x, 0, 30}], x] (* G. C. Greubel, May 28 2019 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec(1/(2-sqrt(1-4*x))) \\ G. C. Greubel, May 28 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/(2-Sqrt(1-4*x)) )); // G. C. Greubel, May 28 2019
(Sage) (1/(2-sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 28 2019
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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