

A135413


Number of at most 4way 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
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OFFSET

1,2


COMMENTS

Obtained by Lagrange inversion of the generating function for at most kway branching trees.
Solve z = T/(1+T+...T^k) when k = 4. I.e., the nth term is the coefficient of x^{n1} 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^(n1) ] (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, n1) ; 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



