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A032009 Number of planted planar trees (n+1 nodes) where any 2 subtrees extending from the same node have a different number of nodes. 3
1, 1, 1, 3, 5, 13, 35, 95, 249, 691, 2007, 5719, 16823, 49371, 146755, 438301, 1319343, 3981699, 12129477, 36987253, 113456615, 348921105, 1077206189, 3332120237, 10347481901, 32183230157, 100372658801, 313633257399, 982232930081, 3080379360481, 9681909324247 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Number of compositions of n-1 into distinct parts if there are a(i) kinds of part i. a(6) = 13: 5, 5', 5'', 5''', 5'''', 41, 4'1, 4''1, 14, 14', 14'', 32, 23.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1938

Index entries for sequences related to rooted trees

FORMULA

Shifts left under "AFK" (ordered, size, unlabeled) transform

MAPLE

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

      b(n, i-1, p) +`if`(i>n, 0, a(i)*b(n-i, i-1, p+1))))

    end:

a:= n-> b(n-1$2, 0):

seq(a(n), n=1..40);  # Alois P. Heinz, Sep 05 2015

MATHEMATICA

b[n_, i_, p_] := b[n, i, p] = If[n==0, p!, If[i<1, 0, b[n, i-1, p] + If[ i>n, 0, a[i]*b[n-i, i-1, p+1]]]]; a[n_] := b[n-1, n-1, 0]; Table[a[n], {n, 1, 40}] (* Jean-Fran├žois Alcover, Feb 24 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A261894.

Sequence in context: A296023 A027039 A283844 * A032027 A005383 A175257

Adjacent sequences:  A032006 A032007 A032008 * A032010 A032011 A032012

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower

EXTENSIONS

More terms from Alois P. Heinz, Sep 05 2015

STATUS

approved

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Last modified February 24 17:22 EST 2018. Contains 299624 sequences. (Running on oeis4.)