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A245750 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 5.

%I A245750 #9 Aug 28 2021 06:43:56
%S A245750 1,7,26,91,291,885,2588,7373,20555,56413,152812,409696,1089029,
%T A245750 2874506,7542257,19690939,51188137,132579401,342294012,881292334,
%U A245750 2263535926,5801350565,14840644204,37901021924,96650247055,246137463494,626087267035,1590840361215
%N A245750 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 5.
%H A245750 Alois P. Heinz, <a href="/A245750/b245750.txt">Table of n, a(n) for n = 15..1000</a>
%p A245750 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A245750       `if`(i<1, 0, add(binomial(b(i-1$2, k$2), j)*
%p A245750        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A245750     end:
%p A245750 a:= n-> b(n-1$2, 5$2) -b(n-1$2, 4$2):
%p A245750 seq(a(n), n=15..60);
%t A245750 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 A245750 a[n_] := b[n-1, n-1, 5, 5] - b[n-1, n-1, 4, 4];
%t A245750 Table[a[n], {n, 15, 60}] (* _Jean-François Alcover_, Aug 28 2021, after Maple code *)
%Y A245750 Column k=5 of A244523.
%K A245750 nonn
%O A245750 15,2
%A A245750 _Joerg Arndt_ and _Alois P. Heinz_, Jul 31 2014