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Search: id:A076540
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| A076540 |
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Number of branches in all ordered trees with n edges. |
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+0
5
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| 1, 3, 11, 41, 154, 582, 2211, 8437, 32318, 124202, 478686, 1849498, 7161556, 27784460, 107980515, 420300045, 1638238710, 6393535170, 24980504010, 97704407790, 382509199020, 1498824792660, 5877754713870, 23067328421826
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Binomial[2n-1,n-2]+binomial[2n-2,n-1]. - David Callan (callan(AT)stat.wisc.edu), Nov 06 2003
Row sums of triangle A136535 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 04 2008
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REFERENCES
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J. Riordan, J. Combinat. Theory, Ser A, 19, 214-222, 1975.
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FORMULA
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a(n)=(3n^2-2n+1)binom(2n, n)/[2(n+1)(2n-1)]; g.f.=(1-z)(C-1)/sqrt(1-4z), where C=[1-sqrt(1-4z)]/(2z) is the Catalan function.
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EXAMPLE
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a(3)=11 because the five ordered trees with 3 edges have 1+3+2+2+3=11 branches altogether.
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CROSSREFS
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First differences of A001791. First differences are in A073663.
Cf. A136535.
Adjacent sequences: A076537 A076538 A076539 this_sequence A076541 A076542 A076543
Sequence in context: A001835 A079935 A113437 this_sequence A129637 A084077 A027103
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 18 2002
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