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%I #37 Apr 18 2017 07:02:29
%S 1,3,8,28,124,668,4248,31176,259488,2416032,24886080,281004480,
%T 3451887360,45832538880,654109585920,9986000371200,162391354675200,
%U 2802498609254400,51156349822771200,984775394044108800,19938798081699840000,423580563732049920000
%N a(n) = n! * (1 + 2*Sum_{k=1..n} 1/k).
%C a(n-1) equals -1 times the coefficient of x of the characteristic polynomial of the n X n matrix whose (i,j)-entry is equal to i if i=j and is equal to 1 otherwise. - _John M. Campbell_, May 23 2011
%H Nathaniel Johnston, <a href="/A000776/b000776.txt">Table of n, a(n) for n = 0..250</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=140">Encyclopedia of Combinatorial Structures 140</a>
%H J. R. Stembridge, <a href="http://dx.doi.org/10.1090/S0002-9947-97-01805-9">Some combinatorial aspects of reduced words in finite Coxeter groups</a>, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.
%F E.g.f. (with offset 1): log(1-x)*(log(1-x)-1). - _Vladeta Jovovic_, Nov 19 2009
%F a(0)=1, a(n+1) = (n+1)*a(n) + 2*n!, n > 0. - _Sean A. Irvine_, Jun 14 2011
%p a := proc(n) option remember: if(n=0)then return 1: fi: return n*a(n-1)+2*(n-1)!: end: seq(a(n),n=0..21); # _Nathaniel Johnston_, Jun 14 2011
%t Table[-Coefficient[CharacteristicPolynomial[Array[KroneckerDelta[#1, #2] (((#1)) - 1) + 1 &, {n, n}], x], x], {n, 1, 10}] (* _John M. Campbell_, May 23 2011 *)
%t Table[n! (1 + 2 HarmonicNumber[n]), {n, 0, 30}] (* _Jean-François Alcover_, Feb 11 2016 *)
%Y Cf. A000774.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E Incorrect formula deleted by _Mark van Hoeij_, Nov 11 2009
%E Offset corrected by _Gary Detlefs_, Jul 13 2010
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