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A245747 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 2.

%I A245747 #11 Aug 28 2021 06:43:42
%S A245747 1,2,5,10,21,42,87,178,371,773,1630,3447,7346,15712,33790,72922,
%T A245747 158020,343494,749101,1638102,3591723,7893801,17387930,38379199,
%U A245747 84875595,188036829,417284180,927469844,2064465340,4601670624,10270463564,22950838754,51346678940
%N A245747 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 2.
%H A245747 Alois P. Heinz, <a href="/A245747/b245747.txt">Table of n, a(n) for n = 4..1000</a>
%F A245747 a(n) = A063895(n+1)-1.
%p A245747 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A245747       `if`(i<1, 0, add(binomial(b(i-1$2, k$2), j)*
%p A245747        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A245747     end:
%p A245747 a:= n-> b(n-1$2, 2$2) -b(n-1$2, 1$2):
%p A245747 seq(a(n), n=4..60);
%t A245747 b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[ b[i-1, i-1, k, k], j]*b[n-i*j, i-1, t - j, k], {j, 0, Min[t, n/i]}]]];
%t A245747 a[n_] :=  b[n-1, n-1, 2, 2] - b[n-1, n-1, 1, 1];
%t A245747 Table[a[n], {n, 4, 60}] (* _Jean-François Alcover_, Aug 28 2021, after Maple code *)
%Y A245747 Column k=2 of A244523.
%K A245747 nonn
%O A245747 4,2
%A A245747 _Joerg Arndt_ and _Alois P. Heinz_, Jul 31 2014