A114870 - OEIS

%I #20 Oct 13 2016 10:30:42

%S 0,1,5,25,141,911,6703,55581,513929,5248891,58724211,714554633,

%T 9397715341,132870076119,2009977939271,32396622193141,554297204755473,

%U 10034223725151731,191617109450287579,3849745645109036001

%N a(n) = A002627(n+1) - A002627(n) - n!.

%H Vincenzo Librandi, <a href="/A114870/b114870.txt">Table of n, a(n) for n = 0..300</a>

%F E.g.f.: (exp(x)-1)/(1-x)^2. - _Vaclav Kotesovec_, Nov 20 2012

%F a(n) = Sum_{k=0..n-1} C(n,k)*(k+1)! = Sum_{k=0..n-1} A074909(n-1,k)*(k+1)!. - _Anton Zakharov_, Sep 26 2016

%t CoefficientList[Series[(E^x-1)/(1-x)^2,{x,0,20}],x]*Range[0,20]! (* _Vaclav Kotesovec_, Nov 20 2012 *)

%t Table[Sum[Binomial[n, k] (k + 1)!, {k, 0, n - 1}], {n, 0, 19}] (* _Michael De Vlieger_, Sep 27 2016 *)

%Y Cf. A002627, A000522, A074909.

%K nonn

%O 0,3

%A _Creighton Dement_, Feb 20 2006