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A244458 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 4.

%I A244458 #12 Feb 06 2015 08:12:13
%S A244458 1,0,0,0,1,2,2,2,4,7,12,16,25,38,61,94,147,227,356,550,862,1345,2113,
%T A244458 3299,5168,8091,12721,19981,31421,49384,77761,122487,193151,304623,
%U A244458 480852,759367,1200150,1897594,3002329,4752436,7527155,11927290,18909719,29993579
%N A244458 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 4.
%H A244458 Alois P. Heinz, <a href="/A244458/b244458.txt">Table of n, a(n) for n = 5..900</a>
%e A244458 a(9) = 1:
%e A244458          o
%e A244458       / ( ) \
%e A244458      o  o o  o
%e A244458    /( )\
%e A244458   o o o o
%p A244458 b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
%p A244458       1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244458       b(n-i*j, i-1, max(0,t-j), k), j=0..n/i)))
%p A244458     end:
%p A244458 a:= n-> b(n-1$2, 4$2) -b(n-1$2, 5$2):
%p A244458 seq(a(n), n=5..50);
%t A244458 b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]*b[n - i*j, i - 1, Max[0, t - j], k], {j, 0, n/i}]] // FullSimplify]; a[n_] := b[n - 1, n - 1, 4, 4] - b[n - 1, n - 1, 5, 5]; Table[a[n], {n, 5, 50}] (* _Jean-François Alcover_, Feb 06 2015, after Maple *)
%Y A244458 Column k=4 of A244454.
%Y A244458 Cf. A244533.
%K A244458 nonn
%O A244458 5,6
%A A244458 _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014