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A216413
Number of forests of trees on n labeled nodes in which each tree has a distinct number of vertices.
1
1, 1, 1, 6, 28, 235, 2466, 31864, 488328, 8901981, 183417490, 4300791946, 111621409956, 3214239089659, 100662133475372, 3440691046061130, 126342964714732576, 4999000389915029881, 210671936366279249610, 9474491260037610708598, 450638933972015166026220
OFFSET
0,4
LINKS
FORMULA
E.g.f.: Product_{n>=1} (1 + n^(n-2)*x^n/n!).
MAPLE
a:= n-> n!*coeff(series(mul(1+k^(k-2)*x^k/k!, k=1..n), x, n+1), x, n):
seq(a(n), n=0..20); # Alois P. Heinz, Sep 07 2012
MATHEMATICA
nn=20; p=Product[1+n^(n-2)x^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[p, {x, 0, nn}], x]
CROSSREFS
Cf. A001858.
Sequence in context: A347770 A206708 A336565 * A090898 A134872 A281003
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Sep 07 2012
STATUS
approved