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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 (list; graph; refs; listen; history; text; internal format)
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: A052593 A052586 A052554 * A249786 A292934 A195203

Adjacent sequences:  A228156 A228157 A228158 * A228160 A228161 A228162

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Aug 14 2013

STATUS

approved

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Last modified June 17 15:38 EDT 2021. Contains 345085 sequences. (Running on oeis4.)