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A007114 Expansion of e.g.f. (1 - x)^x.
(Formerly M0601)
2
1, 0, -2, -3, 4, 30, 66, 0, -496, -1512, 1800, 51480, 487752, 4633200, 50605296, 620703720, 8278947840, 118504008000, 1811156124096, 29452505385600, 507926275873920, 9260774050469760, 178004846331607680, 3597786477984061440, 76284908749415574144, 1693206585883612800000, 39264054809925638534400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

It appears that a(n) is always positive for n > 9.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

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

Branko Dragovich, On Summation of p-Adic Series, arXiv:1702.02569 [math.NT], 2017.

FORMULA

a(n) = Sum_{k=0..n} (-1)^k * A008275(k,n-k) n!/k!. - Max Alekseyev, Aug 10 2013

a(n) ~ 2 * n! / n^3 * (1 + (17/2-3*log(n)-3*gamma)/n), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Apr 21 2014

MATHEMATICA

CoefficientList[Series[(1-x)^x, {x, 0, 30}], x]*Table[(n-1)!, {n, 1, 31}] (* Vincenzo Librandi, Jun 16 2012 *)

PROG

(PARI) a(n) = sum(k=0, n, (-1)^k*stirling(k, n-k)*n!/k!) \\ Max Alekseyev, Aug 10 2013

(PARI) x='x+O('x^33); Vec(serlaplace(exp(x*log(1 - x)))) \\ Joerg Arndt, Apr 01 2017

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1-x)^x)); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 30 2018

CROSSREFS

Sequence in context: A024633 A326829 A064858 * A191471 A305205 A064889

Adjacent sequences:  A007111 A007112 A007113 * A007115 A007116 A007117

KEYWORD

sign

AUTHOR

Simon Plouffe

EXTENSIONS

Signs from Christian G. Bower, Nov 15 1998

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)