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A053490 Expansion of e.g.f.: (1-x)^(-3x). 4
1, 0, 6, 9, 132, 630, 6642, 55440, 608976, 6790392, 85413960, 1145077560, 16600386888, 256806229680, 4233767671728, 74015194485960, 1368023697469440, 26649263762049600, 545697922821501888, 11717708270380421760, 263276186128105633920 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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

MATHEMATICA

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

PROG

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

(MAGMA) m:=30; R<x>:=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

CROSSREFS

Cf. A007113, A053489.

Sequence in context: A121233 A156180 A191011 * A265383 A264375 A061110

Adjacent sequences:  A053487 A053488 A053489 * A053491 A053492 A053493

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified October 15 13:52 EDT 2018. Contains 316236 sequences. (Running on oeis4.)