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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 (list; graph; refs; listen; history; text; internal format)
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: A052395 A034660 A206708 * A090898 A134872 A281003

Adjacent sequences:  A216410 A216411 A216412 * A216414 A216415 A216416

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Sep 07 2012

STATUS

approved

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Last modified November 19 18:39 EST 2019. Contains 329323 sequences. (Running on oeis4.)