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Expansion of e.g.f. (1-x)/(1-5x+3x^2).
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%I #19 May 19 2023 04:16:41

%S 1,4,34,438,7536,162120,4185360,126060480,4339278720,168038478720,

%T 7230318681600,342214829510400,17669683572710400,988372892015308800,

%U 59538455210371737600,3842709218808235776000,264549049753191211008000

%N Expansion of e.g.f. (1-x)/(1-5x+3x^2).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=575">Encyclopedia of Combinatorial Structures 575</a> [broken link].

%F E.g.f.: -(-1+x)/(1-5*x+3*x^2).

%F Recurrence: a(0)=1, a(1)=4, (3*n^2+9*n+6)*a(n) +(-10-5*n)*a(n+1) +a(n+2)=0.

%F Sum(-1/13*(-3+_alpha)*_alpha^(-1-n), _alpha=RootOf(1-5*_Z+3*_Z^2))*n!

%F a(n) = n!*A018902(n). - _R. J. Mathar_, Jun 03 2022

%p spec := [S,{S=Sequence(Union(Z,Z,Z,Prod(Z,Sequence(Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%Y Cf. A018902.

%K easy,nonn

%O 0,2

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