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A053489
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Expansion of e.g.f.: (1-x)^(-2x).
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7
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1, 0, 4, 6, 64, 300, 2568, 20160, 193856, 1989792, 22687200, 279956160, 3737966208, 53589444480, 821522026752, 13407498599040, 232106716968960, 4248256958023680, 81968803604600832, 1662870215019018240, 35384007384670648320, 788053048823608565760
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OFFSET
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0,3
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REFERENCES
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R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.3.
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LINKS
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FORMULA
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E.g.f.: (1-x)^(-2*x).
a(n) = (-1)^n*Sum_{k=0..floor(n/2)} 2^k*binomial(n, k)*k!*Stirling1(n-k, k). - Vladeta Jovovic, Dec 19 2004
a(n) ~ n! * n * (1 + (1-2*log(n)-2*gamma)/n), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Apr 21 2014
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MATHEMATICA
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CoefficientList[Series[(1-x)^(-2*x), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Apr 21 2014 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace((1-x)^(-2*x))) \\ G. C. Greubel, Aug 29 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1-x)^(-2*x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 29 2018
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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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