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Search: id:A052584
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| A052584 |
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A simple regular expression in a labeled universe. |
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+0
3
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| 2, 2, 6, 30, 216, 2040, 23760, 327600, 5201280, 93260160, 1861574400, 40914720000, 981474278400, 25512104217600, 714251739801600, 21426244519680000, 685618901839872000, 23310686975127552000
(list; graph; listen)
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OFFSET
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0,1
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 529
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FORMULA
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E.g.f.: (2-4*x+x^2)/(-1+2*x)/(-1+x)
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)}
(1+2^(n-1))*n!
Contribution from Peter Luschny (peter(AT)luschny.de), Apr 20 2009: (Start)
A weighted binomial sum of the Bernoulli numbers A027641/A027642 with A027641(1)=1 (which amounts to the definition B_{n} = B_{n}(1)).
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)
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MAPLE
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spec := [S, {S=Union(Sequence(Prod(Z, Sequence(Z))), Sequence(Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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]
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CROSSREFS
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Sequence in context: A067644 A097801 A164347 this_sequence A094303 A117394 A003308
Adjacent sequences: A052581 A052582 A052583 this_sequence A052585 A052586 A052587
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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