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a(n) = n! * (n + 1 + 2*Sum_{k=1...n} 1/k).
1

%I #19 Jun 21 2015 17:06:34

%S 1,4,12,46,220,1268,8568,66456,582048,5681952,61174080,720089280,

%T 9199906560,126783809280,1874605662720,29601115891200,497155992883200,

%U 8849184886886400,166399076525875200,3296032301811916800,68596838245232640000,1496490349337948160000

%N a(n) = n! * (n + 1 + 2*Sum_{k=1...n} 1/k).

%H T. D. Noe, <a href="/A000775/b000775.txt">Table of n, a(n) for n = 0..100</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.: x/(1-x)+log(1-x)^2. - _Vladeta Jovovic_, Feb 02 2003

%F a(0)=1, a(n+1) = (n+1)*a(n) + (n+3)*n! for n > 0. - _Sean A. Irvine_, Jun 10 2011

%t Table[n! (n + 1 + 2*Sum[1/k, {k, n}]), {n, 0, 20}] (* _T. D. Noe_, Jun 20 2012 *)

%Y Similar to A000774.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E Incorrect formula deleted by _Mark van Hoeij_, Nov 11 2009