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A245749 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 4.

%I A245749 #10 Aug 28 2021 03:31:16
%S A245749 2,6,21,63,185,512,1403,3750,9928,25969,67462,174039,446884,1142457,
%T A245749 2911078,7396049,18746761,47420345,119746936,301941284,760387426,
%U A245749 1912814031,4807298905,12071798139,30292240853,75965728619,190398931985,476980247827,1194401725174
%N A245749 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 4.
%H A245749 Alois P. Heinz, <a href="/A245749/b245749.txt">Table of n, a(n) for n = 11..1000</a>
%F A245749 a(n) = A116380(n) - A116379(n).
%p A245749 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A245749       `if`(i<1, 0, add(binomial(b(i-1$2, k$2), j)*
%p A245749        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A245749     end:
%p A245749 a:= n-> b(n-1$2, 4$2) -b(n-1$2, 3$2):
%p A245749 seq(a(n), n=11..60);
%t A245749 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 A245749 a[n_] :=  b[n-1, n-1, 4, 4] - b[n-1, n-1, 3, 3];
%t A245749 Table[a[n], {n, 11, 60}] (* _Jean-François Alcover_, Aug 28 2021, after Maple code *)
%Y A245749 Column k=4 of A244523.
%K A245749 nonn
%O A245749 11,1
%A A245749 _Joerg Arndt_ and _Alois P. Heinz_, Jul 31 2014