cp's OEIS Frontend

A318520 Number of unlabeled rooted identity trees with n non-binary nodes.

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