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Search: id:A052852
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| A052852 |
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E.g.f.: (x/(1-x))*exp(x/(1-x)) |
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+0
16
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| 0, 1, 4, 21, 136, 1045, 9276, 93289, 1047376, 12975561, 175721140, 2581284541, 40864292184, 693347907421, 12548540320876, 241253367679185, 4909234733857696, 105394372192969489, 2380337795595885156
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A simple grammar.
Number of {121,212}-avoiding n-ary words of length n. - R. Stephan, Apr 20 2004
Contribution from David Angell (angell(AT)maths.unsw.edu.au), Dec 18 2008: (Start)
If n is a positive integer then the infinite continued fraction
(1+n)/(1+(2+n)/(2+(3+n)/(3+...)))
converges to the rational number A052852(n)/A000262(n). (End)
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 820
Index entries for sequences related to Laguerre polynomials
F. Hivert, J.-C. Novelli and J.-Y. Thibon, Commutative combinatorial Hopf algebras
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FORMULA
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Recurrence: {a(1)=1, a(0)=0, (n^2+2*n)*a(n)+(-4-2*n)*a(n+1)+a(n+2)}
a(n)=sum(n!*binomial(n+2, n-m)/m!, m=0..n). - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jun 19 2001
a(n) = n*A002720(n-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 18 2005
Related to an n-dimensional series : for n>=1, a(n)=(n!/e)*sum_{k_n>=k_{n-1}>=...>=k_1>=0}1/(k_n)!) - Benoit Cloitre (abmt(AT)orange.fr), Sep 30 2006
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MAPLE
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spec := [S, {B=Set(C), C=Sequence(Z, 1 <= card), S=Prod(B, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
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Row sums of unsigned triangle A062139 (generalized a=2 Laguerre).
Cf. A000262 [From David Angell (angell(AT)maths.unsw.edu.au), Dec 18 2008]
Sequence in context: A131965 A104982 A001909 this_sequence A121124 A087761 A120368
Adjacent sequences: A052849 A052850 A052851 this_sequence A052853 A052854 A052855
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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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