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

0,4

Links

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

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

Adjacent sequences: A216410 A216411 A216412 * A216414 A216415 A216416

Keyword

nonn

Author

Geoffrey Critzer, Sep 07 2012

Status

approved