A052771 - OEIS

%I #32 Sep 08 2022 08:44:59

%S 0,0,0,6,48,240,960,3360,10752,32256,92160,253440,675840,1757184,

%T 4472832,11182080,27525120,66846720,160432128,381026304,896532480,

%U 2091909120,4844421120,11142168576,25467813888,57881395200,130862284800,294440140800,659545915392

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

%C The old definition of this sequence was "A simple grammar".

%H Vincenzo Librandi, <a href="/A052771/b052771.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=728">Encyclopedia of Combinatorial Structures 728</a>.

%F a(n) = A090802(n, 3).

%F Recurrence: {a(1)=0, a(2)=0, a(3)=6, (-2*n-2)*a(n)+(-2+n)*a(n+1)}.

%F a(n) = n*(n-1)*(n-2)/8 * 2^n. - _Vaclav Kotesovec_, Nov 27 2012

%F 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 From _Amiram Eldar_, Jan 09 2022: (Start)

%F Sum_{n>=3} 1/a(n) = log(2) - 1/2.

%F Sum_{n>=3} (-1)^(n+1)/a(n) = 9*log(3/2) - 7/2. (End)

%p spec := [S,{B=Set(Z),S=Prod(Z,Z,Z,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%t Range[0, 30]! CoefficientList[Series[Exp[x]^2 x^3, {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 06 2012 *)

%o (Magma) [n*(n-1)*(n-2)/8*2^n: n in [0..30]]; // _Vincenzo Librandi_, Dec 06 2012

%Y Cf. A090802.

%K nonn,easy

%O 0,4

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

%E New definition by _Bruno Berselli_, Dec 06 2012

%E More terms from _Vincenzo Librandi_, Dec 06 2012