cp's OEIS Frontend

A292210 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than four.

%I A292210 #6 Sep 11 2017 17:09:52
%S A292210 0,1,1,2,5,11,30,80,228,656,1945,5835,17808,54881,170951,536726,
%T A292210 1697774,5403629,17295686,55630538,179726346,582942079,1897565974,
%U A292210 6196973039,20297954197,66666192488,219505550167,724415274090,2395838962114,7939424272536
%N A292210 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than four.
%H A292210 Alois P. Heinz, <a href="/A292210/b292210.txt">Table of n, a(n) for n = 0..1000</a>
%H A292210 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%p A292210 b:= proc(n, i, v) option remember; `if`(n=0,
%p A292210       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A292210       `if`(v=n, 1, add(binomial(a(i)+j-1, j)*
%p A292210        b(n-i*j, i-1, v-j), j=0..min(n/i, v)))))
%p A292210     end:
%p A292210 a:= proc(n) option remember; `if`(n<2, n,
%p A292210       add(b(n, n+1-j, j), j=2..min(n, 4)))
%p A292210     end:
%p A292210 seq(a(n), n=0..35);
%Y A292210 Column k=4 of A292085.
%K A292210 nonn
%O A292210 0,4
%A A292210 _Alois P. Heinz_, Sep 11 2017