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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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A090802. Sequence in context: A260344 A353247 A262354 * A056289 A056284 A293967 Adjacent sequences: A052768 A052769 A052770 * A052772 A052773 A052774 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

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Last modified November 26 21:15 EST 2022. Contains 358362 sequences. (Running on oeis4.)
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