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A053532
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Expansion of e.g.f.: (1-x)^(-1/2)*exp(-x/2 -x^2/4 -x^3/6).
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3
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1, 0, 0, 0, 3, 12, 60, 360, 2835, 24696, 237384, 2503440, 28941165, 363593340, 4930388892, 71759200968, 1115892704745, 18465120087120, 323965034820720, 6007037150742624, 117377605956803571, 2410702829834021820, 51917379915449131020
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OFFSET
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0,5
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REFERENCES
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R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.15(a), k=4.
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LINKS
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FORMULA
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Conjecture: D-finite with recurrence 2*a(n) +2*(-n+1)*a(n-1) -(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Jul 06 2020
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MATHEMATICA
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With[{m = 30}, CoefficientList[Series[(1-x)^(-1/2)*Exp[-x/2 -x^2/4 -x^3/6], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 15 2019 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec(serlaplace( (1-x)^(-1/2)*exp(-x/2 -x^2/4 -x^3/6) )) \\ G. C. Greubel, May 15 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (1-x)^(-1/2)*Exp(-x/2 -x^2/4 -x^3/6) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019
(Sage) m = 30; T = taylor((1-x)^(-1/2)*exp(-x/2 -x^2/4 -x^3/6), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 15 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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