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A245748 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 3.

%I A245748 #10 Aug 28 2021 06:43:50
%S A245748 1,3,9,25,66,170,431,1076,2665,6560,16067,39219,95476,231970,562736,
%T A245748 1363640,3301586,7988916,19322585,46722160,112955614,273063236,
%U A245748 660116215,1595906490,3858740567,9331539319,22570697689,54605064084,132137719127,319841444030
%N A245748 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 3.
%H A245748 Alois P. Heinz, <a href="/A245748/b245748.txt">Table of n, a(n) for n = 7..1000</a>
%F A245748 a(n) = A116379(n) - A063895(n+1).
%p A245748 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A245748       `if`(i<1, 0, add(binomial(b(i-1$2, k$2), j)*
%p A245748        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A245748     end:
%p A245748 a:= n-> b(n-1$2, 3$2) -b(n-1$2, 2$2):
%p A245748 seq(a(n), n=7..60);
%t A245748 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 A245748 a[n_] := b[n-1, n-1, 3, 3] - b[n-1, n-1, 2, 2];
%t A245748 Table[a[n], {n, 7, 60}] (* _Jean-François Alcover_, Aug 28 2021, after Maple code *)
%Y A245748 Column k=3 of A244523.
%K A245748 nonn
%O A245748 7,2
%A A245748 _Joerg Arndt_ and _Alois P. Heinz_, Jul 31 2014