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Search: id:A036778
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| A036778 |
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Number of labeled rooted trees on 2n+1 nodes each node having an even number of children. |
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+0
2
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| 1, 3, 65, 3787, 427905, 79549811, 22036379521, 8513206310715, 4374455745966593, 2885264091484122979, 2376040584184726335681, 2389484304129542889498923, 2881763610489447544905661825, 4105338427962827177938910410707, 6820519958449287654130653696838145
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 (1993), 1-10, esp. Eq. (16).
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 185 (3.1.82)
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LINKS
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Index entries for sequences related to rooted trees
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FORMULA
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G.f.: REVERT(x/cosh(x)) = sum(n>=0, a(n)*x^(2n+1)/(2n+1)!). - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 15 2003
a(n) = (1/2^(2*n+1)) * Sum_{k=0..2*n+1} (binomial(2*n+1, k)*(2*k-2*n-1)^(2*n).
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MAPLE
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[ seq((1/2^(2*n+1))*add( binomial(2*n+1, j)*(2*j-(2*n+1))^(2*n), j=0..(2*n+1)), n=1..30) ];
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PROGRAM
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(PARI) a(n)=local(X); if(n<0, 0, X=x+O(x^(2*n+1)); (2*n+1)!*polcoeff(serreverse(x/cosh(x)), 2*n+1)) (from Paul Hanna)
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CROSSREFS
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Adjacent sequences: A036775 A036776 A036777 this_sequence A036779 A036780 A036781
Sequence in context: A112000 A012804 A012837 this_sequence A065400 A091470 A028567
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KEYWORD
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nonn,eigen
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Christian G. Bower (bowerc(AT)usa.net), Jan 13 2004
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