Search: id:A052584
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%I A052584
%S A052584 2,2,6,30,216,2040,23760,327600,5201280,93260160,1861574400,
%T A052584 40914720000,981474278400,25512104217600,714251739801600,
%U A052584 21426244519680000,685618901839872000,23310686975127552000
%N A052584 A simple regular expression in a labeled universe.
%H A052584 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=529">
               Encyclopedia of Combinatorial Structures 529</a>
%F A052584 E.g.f.: (2-4*x+x^2)/(-1+2*x)/(-1+x)
%F A052584 Recurrence: {a(1)=2, a(2)=6, a(0)=2, (2*n^2+6*n+4)*a(n)+(-6-3*n)*a(n+1)+a(n+2)}
%F A052584 (1+2^(n-1))*n!
%F A052584 Contribution from Peter Luschny (peter(AT)luschny.de), Apr 20 2009: (Start)
%F A052584 A weighted binomial sum of the Bernoulli numbers A027641/A027642 with 
               A027641(1)=1 (which amounts to the definition B_{n} = B_{n}(1)).
%F A052584 a(n) = Sum_{k=0..n-1} n!*C(n-1,k)*B_{n-k-1}*2^(k+1)/(k+1). (See also 
               A000051.) (End)
%p A052584 spec := [S,{S=Union(Sequence(Prod(Z,Sequence(Z))),Sequence(Z))},labeled]: 
               seq(combstruct[count](spec,size=n), n=0..20);
%p A052584 a := proc(n) if n = 0 then 2 else add(n!*binomial(n-1,k)*bernoulli(n-k-1,
               1)*2^(k+ 1)/(k+1),k=0..n-1) fi end: [From Peter Luschny (peter(AT)luschny.de), 
               Apr 20 2009]
%Y A052584 Sequence in context: A067644 A097801 A164347 this_sequence A094303 A117394 
               A003308
%Y A052584 Adjacent sequences: A052581 A052582 A052583 this_sequence A052585 A052586 
               A052587
%K A052584 easy,nonn
%O A052584 0,1
%A A052584 encyclopedia(AT)pommard.inria.fr, Jan 25 2000

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