This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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