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

0, 0, 0, 6, 48, 240, 960, 3360, 10752, 32256, 92160, 253440, 675840, 1757184, 4472832, 11182080, 27525120, 66846720, 160432128, 381026304, 896532480, 2091909120, 4844421120, 11142168576, 25467813888, 57881395200, 130862284800, 294440140800, 659545915392

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 728.

Crossrefs

Cf. A090802.

Programs

Magma

[n*(n-1)*(n-2)/8*2^n: n in [0..30]]; // Vincenzo Librandi, Dec 06 2012

Maple

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

Mathematica

Range[0, 30]! CoefficientList[Series[Exp[x]^2 x^3, {x, 0, 30}], x] (* Vincenzo Librandi, Dec 06 2012 *)

Formula

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

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

a(n) = n*(n-1)*(n-2)/8 * 2^n. - Vaclav Kotesovec, Nov 27 2012

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - Chai Wah Wu, May 25 2016

From Amiram Eldar, Jan 09 2022: (Start)

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

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

Extensions

New definition by Bruno Berselli, Dec 06 2012

More terms from Vincenzo Librandi, Dec 06 2012