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Search: id:A052517
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| A052517 |
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Number of pairs of cycles of cardinality at least 1. |
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+0
8
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| 0, 0, 2, 6, 22, 100, 548, 3528, 26136, 219168, 2053152, 21257280, 241087680, 2972885760, 39605518080, 566931294720, 8678326003200, 141468564787200, 2446811181158400, 44753976117043200, 863130293635276800
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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G. Boole, A Treatise On The Calculus of Finite Differences, Dover, 1960, p. 30.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 83
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FORMULA
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Recurrence: {a(1)=0, a(0)=0, a(2)=2, (n^2+2*n+1)*a(n+1)+(-2*n-3)*a(n+2)+a(n+3)}
E.g.f.: (ln(1-x))^2. - Michael Somos Feb 05 2004
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MAPLE
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pairsspec := [S, {S=Prod(B, B), B=Cycle(Z)}, labeled]: seq(combstruct[count](pairsspec, size=n), n=0..20);
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PROGRAM
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(PARI) a(n)=if(n<0, 0, n!*sum(k=1, n-1, 1/k/(n-k)))
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CROSSREFS
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Equals 2 * A000254(n+1), n>0.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)
Equals, for n=>2, the second right hand column of A028421.
(End)
Sequence in context: A012266 A009468 A088819 this_sequence A012270 A009585 A012267
Adjacent sequences: A052514 A052515 A052516 this_sequence A052518 A052519 A052520
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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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EXTENSIONS
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Typos in Maple program fixed by Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009
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