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A216187 Number of labeled rooted trees on n nodes such that each internal node has an odd number of children. 1
0, 1, 2, 6, 28, 200, 1926, 22512, 306104, 4770432, 84234250, 1663735040, 36320155092, 867963393024, 22535294920334, 631718010255360, 19016907901995376, 611869203759792128, 20954324710009221138, 761015341362413371392, 29214930870257449355660 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

FORMULA

E.g.f. satisfies: F(x) = x*(sinh(F(x))+1).

EXAMPLE

a(5) = 200: There are three unlabeled rooted trees of 5 nodes with all internal nodes having an odd number of children. They can be labeled respectively in 20 + 120 + 60 = 200 ways.

  ..o............o............o....

  ..|............|.........../|\...

  ..o............o..........o.o.o..

  ./|\...........|..........|......

  o.o.o..........o..........o......

  ...............|.................

  ...............o.................

  ...............|.................

  ...............o.................

MAPLE

a:= n-> n!*coeff(series(RootOf(F=x*(sinh(F)+1), F), x, n+1), x, n):

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 12 2013

MATHEMATICA

nn=12; f[x_]:=Sum[a[n]x^n/n!, {n, 0, nn}]; s=SolveAlways[0==Series[f[x]-x (Sinh[f[x]]+1), {x, 0, nn}], x]; Table[a[n], {n, 0, nn}]/.s

CROSSREFS

Cf. A036778.

Sequence in context: A058128 A229112 A201959 * A178446 A324126 A272662

Adjacent sequences:  A216184 A216185 A216186 * A216188 A216189 A216190

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Mar 11 2013

STATUS

approved

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Last modified October 17 10:07 EDT 2019. Contains 328108 sequences. (Running on oeis4.)