cp's OEIS Frontend

A358072 a(n) is the number of "merger histories" of n elements (see A256006) where at most 3 elements can merge at the same time.

%I A358072 #31 Nov 14 2022 20:03:07
%S A358072 1,1,4,28,320,5360,123760,3765440,145951680,7019678400,410164339200,
%T A358072 28615175635200,2349290700556800,224201377681881600,
%U A358072 24610071925350912000,3078761402543963136000,435446399655217606656000
%N A358072 a(n) is the number of "merger histories" of n elements (see A256006) where at most 3 elements can merge at the same time.
%C A358072 Also the number of unordered, leaf-labeled increasing trees on n leaves with maximum node outdegree 3.
%H A358072 Johannes Wirtz, <a href="/A358072/b358072.txt">Table of n, a(n) for n = 1..1000</a>
%H A358072 Johannes Wirtz, <a href="https://arxiv.org/abs/2211.03632">On the enumeration of leaf-labelled increasing trees with arbitrary node-degree</a>, arXiv:2211.03632 [q-bio.PE], 2022.
%F A358072 a(n) = n*(n-1)*((n-2)*a(n-2) + 3*a(n-1))/6 for n >= 3.
%F A358072 a(n+1) ~ 2*Pi*exp(-2/3)*Gamma(5/3)^(-1)*n^(2n+8/3)*2^(-n)*exp^(-2n).
%F A358072 2*Pi*exp(-2/3)*Gamma(5/3)^(-1) = 3.573427548...
%p A358072 a := proc(n) option remember; if n < 2 then return 1 else
%p A358072 a(n-2)*binomial(n, 3) + a(n-1)*binomial(n, 2) fi end:
%p A358072 seq(a(n), n = 1..17);
%Y A358072 Cf. A256006.
%K A358072 nonn
%O A358072 1,3
%A A358072 _Johannes Wirtz_, Oct 29 2022