A053489 Expansion of e.g.f.: (1-x)^(-2x).

1, 0, 4, 6, 64, 300, 2568, 20160, 193856, 1989792, 22687200, 279956160, 3737966208, 53589444480, 821522026752, 13407498599040, 232106716968960, 4248256958023680, 81968803604600832, 1662870215019018240, 35384007384670648320, 788053048823608565760

Offset: 0

Author

N. J. A. Sloane, Jan 15 2000

Keywords

• nonn

References

• R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.3.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A007113, A053490.

Programs

Magma

m:=30; R:=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

Mathematica

CoefficientList[Series[(1-x)^(-2*x), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Apr 21 2014 *)

PARI

x='x+O('x^30); Vec(serlaplace((1-x)^(-2*x))) \\ G. C. Greubel, Aug 29 2018

Formula

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