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A007113
Expansion of e.g.f. (1 + x)^x.
(Formerly M0919)
18
1, 0, 2, -3, 20, -90, 594, -4200, 34544, -316008, 3207240, -35699400, 432690312, -5672581200, 79991160144, -1207367605080, 19423062612480, -331770360922560, 5997105160795584, -114373526841360000, 2295170834453089920, -48344592370577247360
OFFSET
0,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.3.
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*k!*Stirling1(n-k, k). - Vladeta Jovovic, Dec 19 2004
a(n) ~ (-1)^n * n!. - Vaclav Kotesovec, Jun 06 2019
MAPLE
a:= n-> n! *coeff(series((1+x)^x, x, n+1), x, n):
seq(a(n), n=0..30); # Alois P. Heinz, Dec 12 2012
MATHEMATICA
CoefficientList[Series[(1 + x)^x, {x, 0, 19}], x]*Table[(n - 1)!, {n, 1, 20}]
a[n_] := (-1)^n*n!*Sum[ StirlingS1[n - k, k]/(n - k)!*(-1)^(n - 2*k), {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Dec 12 2012, after Vladeta Jovovic *)
CROSSREFS
Cf. A053489, A053490. Apart from initial terms and signs, same as A066166.
Sequence in context: A264417 A348311 A066166 * A052804 A267652 A258089
KEYWORD
sign
AUTHOR
EXTENSIONS
Signs from Christian G. Bower, Nov 15 1998
STATUS
approved