cp's OEIS Frontend

A236696 Number of forests on n vertices consisting of labeled rooted trees of the same size.

%I A236696 #24 Nov 11 2019 00:30:51
%S A236696 1,3,10,77,626,8707,117650,2242193,43250842,1049248991,25937424602,
%T A236696 772559330281,23298085122482,817466439388341,29223801257127976,
%U A236696 1181267018656911617,48661191875666868482,2232302772999145783735,104127350297911241532842
%N A236696 Number of forests on n vertices consisting of labeled rooted trees of the same size.
%H A236696 Alois P. Heinz, <a href="/A236696/b236696.txt">Table of n, a(n) for n = 1..200</a>
%F A236696 a(n) = sum(d divides n, n!/(n/d)!*(d^(d-1)/d!)^(n/d) ).
%F A236696 E.g.f.: sum(k>=1, exp(k^(k-1)*x^k/k!)).
%e A236696 For n = 3 we have the following 10 forests (where the roots are denoted by ^):
%e A236696                               3  2  3  1  2  1
%e A236696                               |  |  |  |  |  |
%e A236696          2   3  1   3  1   2  2  3  1  3  1  2
%e A236696           \ /    \ /    \ /   |  |  |  |  |  |
%e A236696   1 2 3    1      2      3    1  1  2  2  3  3
%e A236696   ^ ^ ^,   ^,     ^,     ^,   ^, ^, ^, ^, ^, ^
%t A236696 Table[Sum[n!/(n/d)!*(d^(d-1)/d!)^(n/d), {d,Divisors[n]}], {n,1,100}]
%o A236696 (Maxima) a(n):= lsum(n!/(n/d)!*(d^(d-1)/d!)^(n/d),d,listify(divisors(n))); makelist(a(n),n,1,40); /* _Emanuele Munarini_, Feb 03 2014 */
%Y A236696 Cf. A000169, A038041, A005225, A055225.
%K A236696 nonn
%O A236696 1,2
%A A236696 _Emanuele Munarini_, Jan 30 2014