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 A007113 Expansion of e.g.f. (1 + x)^x. (Formerly M0919) 8
 1, 0, 2, -3, 20, -90, 594, -4200, 34544, -316008, 3207240, -35699400, 432690312, -5672581200, 79991160144, -1207367605080, 19423062612480, -331770360922560, 5997105160795584, -114373526841360000, 2295170834453089920, -48344592370577247360 (list; graph; refs; listen; history; text; internal format)
 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 Vincenzo Librandi, Table of n, a(n) for n = 0..200 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 75 FORMULA a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*k!*Stirling1(n-k, k). - Vladeta Jovovic, Dec 19 2004 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: A292122 A264417 A066166 * A052804 A267652 A258089 Adjacent sequences:  A007110 A007111 A007112 * A007114 A007115 A007116 KEYWORD sign AUTHOR EXTENSIONS Signs from Christian G. Bower, Nov 15 1998 STATUS approved

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Last modified October 23 12:10 EDT 2018. Contains 316527 sequences. (Running on oeis4.)