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A135413
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Number of at most 4-way branching ordered (i.e. plane) trees.
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1
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1, 2, 6, 20, 70, 246, 875, 3144, 11385, 41470, 151778, 557712, 2056210, 7602700, 28180050, 104677280, 389571983, 1452293766, 5422187130, 20271296100, 75878518695, 284339792110, 1066585128810, 4004566131000, 15048213795600
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OFFSET
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1,2
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COMMENTS
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Obtained by Lagrange inversion of the generating function for at most k-way branching trees.
Solve z = T/(1+T+...T^k) when k = 4. I.e. the n-th term is the coefficient of x^{n-1} in the expansion of (1+x+x^2+x^3+x^4)^n.
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LINKS
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Table of n, a(n) for n=1..25.
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FORMULA
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a(n) = [ x^(n-1) ] (1+x+x^2+x^3+x^4)^n.
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MAPLE
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A135413 := proc(n) local ogf, i ; ogf := 1 ; for i from 1 to n do ogf := taylor(ogf*(1+x+x^2+x^3+x^4), x=0, n) ; od: coeftayl(ogf, x=0, n-1) ; end: seq(A135413(n), n=1..30) ; # R. J. Mathar, Apr 21 2008
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CROSSREFS
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For k=2 this is A005717, for k=3 this is A005726.
Sequence in context: A148479 A150124 A045631 * A193653 A147748 A150125
Adjacent sequences: A135410 A135411 A135412 * A135414 A135415 A135416
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KEYWORD
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nonn,easy
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AUTHOR
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Andrey Bovykin (indiscernibles(AT)googlemail.com), Mar 01 2008
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EXTENSIONS
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More terms from R. J. Mathar, Apr 21 2008
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STATUS
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approved
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