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A052771
E.g.f.: x^3*exp(x)^2.
3
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
0,4
COMMENTS
The old definition of this sequence was "A simple grammar".
LINKS
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
Cf. A090802.
Sequence in context: A260344 A353247 A262354 * A056289 A056284 A366622
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