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A053490 Expansion of e.g.f.: (1-x)^(-3x). 7
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
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
Sequence in context: A156180 A191011 A351734 * A265383 A367881 A367879
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 15 2000
STATUS
approved

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Last modified February 25 00:32 EST 2024. Contains 370308 sequences. (Running on oeis4.)