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Search: id:A025225
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| A025225 |
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a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 2. Also a(n) = (2^n)*C(n-1), where C = A000108 (Catalan numbers). |
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8
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| 2, 4, 16, 80, 448, 2688, 16896, 109824, 732160, 4978688, 34398208, 240787456, 1704034304, 12171673600, 87636049920, 635361361920, 4634400522240, 33985603829760, 250420238745600, 1853109766717440
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Number of generators of degree n of the Hopf algebra of 2-colored planar binary trees. Also, dimensions of the graded components of the primitive Lie algebra of the same Hopf algebra. - Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 653
J.-C. Novelli and J.-Y. Thibon, Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions
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FORMULA
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G.f.: (1-sqrt(1-8*x))/2 - Michael Somos, Jun 08, 2000.
Given g.f. C(x) and given A(x)= g.f. of A100238, then B(x)=A(x)-1-x satisfies B(x)=x-C(x*B(x)). - Michael Somos Sep 07 2005
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MATHEMATICA
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InverseSeries[Series[y/2-y^2/2, {y, 0, 24}], x] (* then A(x)=y(x) *) - Len Smiley Apr 13 2000
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PROGRAM
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(PARI) a(n)=polcoeff((1-sqrt(1-8*x+x*O(x^n)))/2, n)
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CROSSREFS
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Essentially identical to A115125.
Sequence in context: A102736 A103619 A027436 this_sequence A115125 A000831 A000090
Adjacent sequences: A025222 A025223 A025224 this_sequence A025226 A025227 A025228
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Typo in definition corrected by R. J. Mathar, Aug 11 2008
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