A216413 Number of forests of trees on n labeled nodes in which each tree has a distinct number of vertices.

1, 1, 1, 6, 28, 235, 2466, 31864, 488328, 8901981, 183417490, 4300791946, 111621409956, 3214239089659, 100662133475372, 3440691046061130, 126342964714732576, 4999000389915029881, 210671936366279249610, 9474491260037610708598, 450638933972015166026220

Offset: 0

Author

Geoffrey Critzer, Sep 07 2012

Keywords

• nonn

Links

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

Crossrefs

Cf. A001858.

Programs

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]

Formula

E.g.f.: Product_{n>=1} (1 + n^(n-2)*x^n/n!).