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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 G. C. Greubel and Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 250 terms from G. C. Greubel) 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 MATHEMATICA Join[{1}, Table[Coefficient[(1 + x + x^2 + x^3 + x^4)^n, x, (n - 1)], {n, 2, 25}]] (* G. C. Greubel, Oct 13 2016 *) CROSSREFS For k=2 this is A005717, for k=3 this is A005726. Sequence in context: A045631 A275046 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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