cp's OEIS Frontend

A052771 E.g.f.: x^3*exp(x)^2.

%I A052771 #32 Sep 08 2022 08:44:59
%S A052771 0,0,0,6,48,240,960,3360,10752,32256,92160,253440,675840,1757184,
%T A052771 4472832,11182080,27525120,66846720,160432128,381026304,896532480,
%U A052771 2091909120,4844421120,11142168576,25467813888,57881395200,130862284800,294440140800,659545915392
%N A052771 E.g.f.: x^3*exp(x)^2.
%C A052771 The old definition of this sequence was "A simple grammar".
%H A052771 Vincenzo Librandi, <a href="/A052771/b052771.txt">Table of n, a(n) for n = 0..1000</a>
%H A052771 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=728">Encyclopedia of Combinatorial Structures 728</a>.
%F A052771 a(n) = A090802(n, 3).
%F A052771 Recurrence: {a(1)=0, a(2)=0, a(3)=6, (-2*n-2)*a(n)+(-2+n)*a(n+1)}.
%F A052771 a(n) = n*(n-1)*(n-2)/8 * 2^n. - _Vaclav Kotesovec_, Nov 27 2012
%F A052771 a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - _Chai Wah Wu_, May 25 2016
%F A052771 From _Amiram Eldar_, Jan 09 2022: (Start)
%F A052771 Sum_{n>=3} 1/a(n) = log(2) - 1/2.
%F A052771 Sum_{n>=3} (-1)^(n+1)/a(n) = 9*log(3/2) - 7/2. (End)
%p A052771 spec := [S,{B=Set(Z),S=Prod(Z,Z,Z,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052771 Range[0, 30]! CoefficientList[Series[Exp[x]^2 x^3, {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 06 2012 *)
%o A052771 (Magma) [n*(n-1)*(n-2)/8*2^n: n in [0..30]]; // _Vincenzo Librandi_, Dec 06 2012
%Y A052771 Cf. A090802.
%K A052771 nonn,easy
%O A052771 0,4
%A A052771 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052771 New definition by _Bruno Berselli_, Dec 06 2012
%E A052771 More terms from _Vincenzo Librandi_, Dec 06 2012