A228159 Number of labeled rooted identity trees on n nodes (rooted trees that admit n! labelings).

0, 1, 2, 6, 48, 360, 4320, 60480, 1008000, 18869760, 410054400, 9859449600, 262492876800, 7634327500800, 241483866624000, 8237040844032000, 301832166924288000, 11812023799640064000, 492028821658902528000, 21728004544824754176000, 1014150336304416030720000

Offset

0,3

Comments

a(n) = n! * A004111(n).

Links

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

Formula

E.g.f. A(x) satisfies A(x) = x Product_{n>=1} x*(1 + x^n)^(a(n)/n!).

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(b(i-1$2), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> n!*b(n-1$2):
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 14 2013

Mathematica

nn=20; SolveAlways[
  0 == Series[
    f[x] - x Product[(1 + x^i)^(a[i]/i!), {i, 1, nn}], {x, 0, nn}],
  x]; Table[a[n], {n, 0, nn}] /. sol

Crossrefs

Sequence in context: A358065 A052586 A052554 * A249786 A292934 A394167

Adjacent sequences: A228156 A228157 A228158 * A228160 A228161 A228162

Keyword

nonn

Author

Geoffrey Critzer, Aug 14 2013

Status

approved