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A032305 Number of rooted trees where any 2 subtrees extending from the same node have a different number of nodes. 9
1, 1, 1, 2, 3, 6, 12, 25, 51, 111, 240, 533, 1181, 2671, 6014, 13795, 31480, 72905, 168361, 393077, 914784, 2150810, 5040953, 11914240, 28089793, 66702160, 158013093, 376777192, 896262811, 2144279852, 5120176632, 12286984432, 29428496034, 70815501209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for sequences related to rooted trees

FORMULA

Shifts left under "EFK" (unordered, size, unlabeled) transform.

G.f.: A(x) = x*Product_{n>=1} (1+a(n)*x^n) = Sum_{n>=1} a(n)*x^n. - Paul D. Hanna, Apr 07 2004

MAPLE

A:= proc(n) if n<=1 then x else convert(series(x* (product(1+ coeff(A(n-1), x, i)*x^i, i=1..n-1)), x=0, n+1), polynom) fi end: a:= n-> coeff(A(n), x, n): seq(a(n), n=1..31);  # Alois P. Heinz, Aug 22 2008

# second Maple program:

g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(`if`(j=0, 1, g((i-1)$2))*g(n-i*j, i-1), j=0..min(1, n/i))))

    end:

a:= n-> g((n-1)$2):

seq(a(n), n=1..35);  # Alois P. Heinz, Mar 04 2013

MATHEMATICA

nn=30; f[x_]:=Sum[a[n]x^n, {n, 0, nn}]; sol=SolveAlways[0 == Series[f[x]-x Product[1+a[i]x^i, {i, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}]/.sol  (* Geoffrey Critzer, Nov 17 2012 *)

PROG

(PARI) a(n)=polcoeff(x*prod(i=1, n-1, 1+a(i)*x^i)+x*O(x^n), n)

CROSSREFS

Cf. A000081, A213920.

Sequence in context: A216632 A077903 A038086 * A032218 A005829 A038087

Adjacent sequences:  A032302 A032303 A032304 * A032306 A032307 A032308

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.