%I #7 Aug 28 2018 18:04:36
%S 0,1,1,1,1,1,1,2,3,5,8,14,23,40,69,122,215,382,679,1217,2185,3944,
%T 7136,12958,23578,43026,78673,144190,264755,487074,897549,1656697,
%U 3062423,5669110,10508397,19503447,36240898,67418514,125551221,234047825,436722486
%N Number of unlabeled rooted identity trees with n non-binary nodes.
%H Alois P. Heinz, <a href="/A318520/b318520.txt">Table of n, a(n) for n = 0..3501</a>
%e a(8) = 3: o o o
%e | | /|\
%e o o o o o
%e | /|\ | |
%e o o o o o o
%e | | | |
%e o o o o
%e | | |
%e o o o
%e |
%e o
%e |
%e o
%e |
%e o
%p b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=1, 0, 1), `if`(i<1, 0,
%p add(b(n-i*j, i-1, max(0, t-j))*binomial(a(i), j), j=0..n/i)))
%p end:
%p a:= n-> `if`(n<2, n, b(n-1$2, 3)):
%p seq(a(n), n=0..50);
%Y Cf. A000081, A004111, A303023.
%K nonn
%O 0,8
%A _Alois P. Heinz_, Aug 28 2018
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