cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A216413 #24 Mar 18 2018 15:13:02
%S A216413 1,1,1,6,28,235,2466,31864,488328,8901981,183417490,4300791946,
%T A216413 111621409956,3214239089659,100662133475372,3440691046061130,
%U A216413 126342964714732576,4999000389915029881,210671936366279249610,9474491260037610708598,450638933972015166026220
%N A216413 Number of forests of trees on n labeled nodes in which each tree has a distinct number of vertices.
%H A216413 Alois P. Heinz, <a href="/A216413/b216413.txt">Table of n, a(n) for n = 0..150</a>
%F A216413 E.g.f.: Product_{n>=1} (1 + n^(n-2)*x^n/n!).
%p A216413 a:= n-> n!*coeff(series(mul(1+k^(k-2)*x^k/k!, k=1..n), x, n+1), x, n):
%p A216413 seq(a(n), n=0..20);  # _Alois P. Heinz_, Sep 07 2012
%t A216413 nn=20;p=Product[1+n^(n-2)x^n/n!,{n,1,nn}];Range[0,nn]! CoefficientList[Series[p,{x,0,nn}],x]
%Y A216413 Cf. A001858.
%K A216413 nonn
%O A216413 0,4
%A A216413 _Geoffrey Critzer_, Sep 07 2012