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%I #18 Sep 08 2022 08:44:31
%S 1,1,4,21,124,705,3726,18361,85240,376641,1597690,6551721,26116740,
%T 101647585,387634534,1452554265,5360857456,19523426433,70272302706,
%U 250318462537,883418329660,3091835703201,10739780397214
%N Expansion of e.g.f.: 1 + x*exp(x) + x^2*exp(2*x) + x^3*exp(3*x).
%H Vincenzo Librandi, <a href="/A003014/b003014.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (20,-175,878,-2779,5744,-7737,6534,-3132,648).
%F a(n) = n + n*(n-1)*2^(n-2) + n*(n-1)*(n-2)*3^(n-3). - _Ralf Stephan_, Mar 24 2004
%t With[{nn=30},CoefficientList[Series[1+x Exp[x]+x^2 Exp[2x]+x^3 Exp[3x],{x,0,nn}],x] Range[0,nn]!] (* or *) LinearRecurrence[{20,-175,878,-2779,5744,-7737,6534,-3132,648},{1,1,4,21,124,705,3726,18361,85240,376641},30] (* _Harvey P. Dale_, Mar 29 2016 *)
%o (Magma) [1],[(n+1) + n*(n+1)*2^(n-1) + n*(n+1)*(n-1)*3^(n-2) : n in [0..30]]; // _Vincenzo Librandi_, Oct 08 2011
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E Definition clarified by _Harvey P. Dale_, Mar 29 2016
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