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A228159
Number of labeled rooted identity trees on n nodes (rooted trees that admit n! labelings).
2
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
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 A195203
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Aug 14 2013
STATUS
approved