%I M3950 #28 Nov 03 2017 22:18:11
%S 1,5,28,180,1320,10920,100800,1028160,11491200,139708800,1836172800,
%T 25945920000,392302310400,6320426112000,108101081088000,
%U 1956280854528000,37347179950080000,750144785854464000,15813863053148160000,349121438173347840000
%N a(n+1) = (n-1)*a(n) + n*n!.
%C Number of ascending runs of length at least two in all permutations of [n]. Example: a(3)=5 because we have (123), (13)2, 3(12), 2(13), (23)1 and 321, where the ascending runs of length at least 2 are shown between parentheses. - _Emeric Deutsch_ and _Ira M. Gessel_, Sep 07 2004
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H J. Francon, <a href="http://www.numdam.org/item?id=ITA_1978__12_1_49_0">Histoires de fichiers</a>, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62.
%H J. Francon, <a href="/A006157/a006157.pdf">Histoires de fichiers</a>, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62. (Annotated scanned copy)
%F a(n) = (2n-1)/6 * n!.
%F E.g.f.: x^2*(3-x)/(6*(1-x)^2). - _Emeric Deutsch_ and _Ira M. Gessel_, Sep 07 2004
%t Table[(2n-1)/6*n!,{n,2,30}] (* _Harvey P. Dale_, Jan 06 2014 *)
%Y Cf. A014484.
%K nonn,easy
%O 2,2
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from _Harvey P. Dale_, Jan 06 2014