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A135413 Number of at most 4-way branching ordered (i.e. plane) trees. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..25.

FORMULA

a(n) = [ x^(n-1) ] (1+x+x^2+x^3+x^4)^n.

MAPLE

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

CROSSREFS

For k=2 this is A005717, for k=3 this is A005726.

Sequence in context: A150124 A045631 A229472 * A193653 A147748 A150125

Adjacent sequences:  A135410 A135411 A135412 * A135414 A135415 A135416

KEYWORD

nonn,easy

AUTHOR

Andrey Bovykin (indiscernibles(AT)googlemail.com), Mar 01 2008

EXTENSIONS

More terms from R. J. Mathar, Apr 21 2008

STATUS

approved

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Last modified July 30 13:12 EDT 2014. Contains 245069 sequences.