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%I #22 Oct 30 2022 10:02:57
%S 1,1,4,30,312,4080,64080,1174320,24595200,579519360,15172012800,
%T 436929292800,13726748851200,467182235520000,17123385600921600,
%U 672444082582272000,28167703419727872000,1253648083943743488000
%N Expansion of e.g.f. (1-2x)/(1-3x+x^2).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=517">Encyclopedia of Combinatorial Structures 517</a>
%H Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.
%F E.g.f.: -(-1+2*x)/(1-3*x+x^2).
%F Recurrence: {a(1)=1, a(0)=1, (n^2+3*n+2)*a(n)+(-6-3*n)*a(n+1)+a(n+2)=0}.
%F Sum((1/5)*(-1+4*_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2-3*_Z+1))*n!.
%F a(n) = n!*Sum_{k=1..n} binomial(n-1,k-1)*Fibonacci(k); n>0. [_Vladimir Kruchinin_, Sep 01 2010]
%F a(n) = n!*A001519(n). - _R. J. Mathar_, Nov 27 2011
%p spec := [S,{S=Sequence(Prod(Z,Sequence(Prod(Z,Sequence(Z)))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000