A053490 Expansion of e.g.f.: (1-x)^(-3x).

1, 0, 6, 9, 132, 630, 6642, 55440, 608976, 6790392, 85413960, 1145077560, 16600386888, 256806229680, 4233767671728, 74015194485960, 1368023697469440, 26649263762049600, 545697922821501888, 11717708270380421760, 263276186128105633920

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, A053489.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1-x)^(-3*x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 29 2018

Mathematica

CoefficientList[Series[(1-x)^(-3*x), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Apr 21 2014 *)

PARI

x='x+O('x^30); Vec(serlaplace((1-x)^(-3*x))) \\ G. C. Greubel, Aug 29 2018

Formula

a(n) = (-1)^n*Sum_{k=0..floor(n/2)} 3^k*binomial(n, k)*k!*Stirling1(n-k, k). - Vladeta Jovovic, Dec 19 2004

a(n) ~ n! * n^2/2 * (1 + (9-6*log(n)-6*gamma)/n), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Apr 21 2014