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Search: id:A052524
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| A052524 |
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Number of ordered labeled rooted trees on n nodes with non-leaf nodes having more than two children. |
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+0
3
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| 0, 1, 0, 6, 24, 480, 5760, 126000, 2580480, 69310080, 1959552000, 64505548800, 2292022656000, 90366525849600, 3843167789260800, 177248722210560000, 8758468152225792000, 463225965106544640000, 26058454876652470272000
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The correspondence between rooted trees and dissection of (n+1)-gon as in A046736 is just like the case for Catalan numbers and binary trees.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 94
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FORMULA
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E.g.f.: A(x)=sum_{n>0} a(n)x^n/n! satisfies A(x)-A(x)^2-A(x)^3 = x*(1-A(x)).
Recurrence: a(0)=0, a(1)=1, a(2)=0, a(3)=6, 8*n*(n+1)*(n+2)*(1-2*n)*a(n)+6*(13*n+10)*(2*n+1)*(n+2)*a(n+1)-24*(2*n+5)*(4*n+7)*a(n+2)-4*(19*n+40)*a(n+3)+35*a(n+4)=0
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MAPLE
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spec := [S, {S=Union(Z, Sequence(S, card >= 3))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROGRAM
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(PARI) a(n)=if(n<1, 0, n!*polcoeff(serreverse((x-x^2-x^3)/(1-x)+O(x^(n+2))), n))
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CROSSREFS
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a(n)=n!*A046736(n+1) for n>0.
Sequence in context: A152886 A128614 A139240 this_sequence A036284 A139235 A136606
Adjacent sequences: A052521 A052522 A052523 this_sequence A052525 A052526 A052527
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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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