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A007788
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Number of augmented Andre 3-signed permutations: E.g.f. (1-sin(3*x))^(-1/3).
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8
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1, 1, 4, 19, 136, 1201, 13024, 165619, 2425216, 40132801, 740882944, 15091932019, 336257744896, 8134269015601, 212309523595264, 5946914908771219, 177934946000306176, 5663754614516217601
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OFFSET
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0,3
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COMMENTS
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It appears that all members are of the form 3k+1. - Ralf Stephan, Nov 12 2007
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LINKS
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FORMULA
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E.g.f.: (1-sin(3*x))^(-1/3).
a(n) ~ n! * 2*6^n/(Pi^(n+2/3)*n^(1/3)*Gamma(2/3)). - Vaclav Kotesovec, Jun 25 2013
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MAPLE
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m:=20; S:=series( (1-sin(3*x))^(-1/3), x, m+1): seq(j!*coeff(S, x, j), j=0..m); # G. C. Greubel, Mar 05 2020
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[(1-Sin[3x])^(-1/3), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 23 2011 *)
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PROG
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(PARI) Vec(serlaplace( (1-sin(3*x))^(-1/3) +O('x^20) )) \\ G. C. Greubel, Mar 05 2020
(Magma) R<x>:=PowerSeriesRing(Rationals(), 20); Coefficients(R!(Laplace( (1-Sin(3*x))^(-1/3) ))); // G. C. Greubel, Mar 05 2020
(Sage)
m=20;
P.<x> = PowerSeriesRing(QQ, prec)
return P( (1-sin(3*x))^(-1/3) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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R. Ehrenborg (ehrenbor(AT)lacim.uqam.ca) and M. A. Readdy (readdy(AT)lacim.uqam.ca)
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STATUS
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approved
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