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A244533 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 4.

%I A244533 #13 Feb 06 2015 09:15:25
%S A244533 1,0,0,0,4,9,10,11,34,91,196,330,636,1377,2976,6061,12199,25186,52767,
%T A244533 109066,224964,467605,979056,2042847,4244986,8844130,18527956,
%U A244533 38878929,81460220,170576593,357894472,752544917,1583579674,3332453026,7016669752,14790212086
%N A244533 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 4.
%H A244533 Alois P. Heinz, <a href="/A244533/b244533.txt">Table of n, a(n) for n = 5..1000</a>
%H A244533 Vaclav Kotesovec, <a href="/A244533/a244533.txt">Recurrence (of order 11)</a>
%F A244533 a(n) ~ c * d^n / (sqrt(Pi) * n^(3/2)), where d = 2.18452974131524781307797151868229485574758... is the root of the equation -229 - 36*d + 2*d^2 - 32*d^3 + 19*d^4 + 4*d^5 = 0, and c = 0.181069926661856899940163775713243367029404419526724... . - _Vaclav Kotesovec_, Jul 02 2014
%p A244533 b:= proc(n, t, k) option remember; `if`(n=0,
%p A244533       `if`(t in [0, k], 1, 0), `if`(t>n, 0, add(b(j-1, k$2)*
%p A244533        b(n-j, max(0, t-1), k), j=1..n)))
%p A244533     end:
%p A244533 a:= n-> b(n-1, 4$2) -b(n-1, 5$2):
%p A244533 seq(a(n), n=5..45);
%t A244533 b[n_, t_, k_] := b[n, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[t > n, 0, Sum[b[j - 1, k, k]*b[n - j, Max[0, t - 1], k], {j, 1, n}]]]; T[n_, k_] := b[n - 1, k, k] - If[n == 1 && k == 0, 0, b[n - 1, k + 1, k + 1]]; a[n_] := b[n - 1, 4, 4] - b[n - 1, 5, 5]; Table[a[n], {n, 5, 45}] (* _Jean-François Alcover_, Feb 06 2015, after Maple *)
%Y A244533 Column k=4 of A244530.
%Y A244533 Cf. A244458.
%K A244533 nonn
%O A244533 5,5
%A A244533 _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014