OFFSET
0,4
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.
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)
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 *)
PROG
(Magma) [n*(n-1)*(n-2)/8*2^n: n in [0..30]]; // Vincenzo Librandi, Dec 06 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New definition by Bruno Berselli, Dec 06 2012
More terms from Vincenzo Librandi, Dec 06 2012
STATUS
approved