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E.g.f.: x^3*(exp(x)-1)^2.
2

%I #22 Jan 02 2020 16:13:19

%S 0,0,0,0,0,120,720,2940,10080,31248,90720,251460,673200,1753752,

%T 4468464,11176620,27518400,66838560,160422336,381014676,896518800,

%U 2091893160,4844402640,11142147324,25467789600,57881367600,130862253600,294440105700,659545876080

%N E.g.f.: x^3*(exp(x)-1)^2.

%C Previous name was: A simple grammar.

%H Andrew Howroyd, <a href="/A052769/b052769.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=726">Encyclopedia of Combinatorial Structures 726</a>

%F E.g.f.: x^3*exp(x)^2 - 2*x^3*exp(x) + x^3.

%F Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, (2*n^2+6*n+4)*a(n)+(-3*n^2+12)*a(n+1)+(-3*n+n^2+2)*a(n+2), a(5)= 120}.

%F For n<>3, a(n) = (2^n-16)*(n-2)*(n-1)*n/8. - _Vaclav Kotesovec_, Sep 30 2013

%p spec := [S,{B=Set(Z,1 <= card),S=Prod(Z,Z,Z,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%t CoefficientList[Series[x^3*(E^x-1)^2, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 30 2013 *)

%o (PARI) seq(n)={Vec(serlaplace(x^3*(exp(x + O(x^(n-3)))-1)^2), -(n+1))} \\ _Andrew Howroyd_, Jan 02 2020

%K easy,nonn

%O 0,6

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

%E New name, using e.g.f., by _Vaclav Kotesovec_, Sep 30 2013

%E Terms a(21) and beyond from _Andrew Howroyd_, Jan 02 2020