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A003014 Expansion of e.g.f.: 1 + x*exp(x) + x^2*exp(2*x) + x^3*exp(3*x). 1

%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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Last modified July 12 16:40 EDT 2024. Contains 374251 sequences. (Running on oeis4.)