This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381523 #7 Feb 26 2025 09:51:17
%S A381523 1,1,35,8925,8033025,19010866875,97622651251125,958647115051250625,
%T A381523 16437666902498106890625,459581350409578975249546875,
%U A381523 19861812620603175030206132109375,1271123241419341933758758697996796875,116303414318027015186301064741488195703125,14773177703549629967524262172307456486365234375
%N A381523 Number of labeled histories for rooted 4-furcating trees with 3n+1 leaves if simultaneous 4-furcations are allowed.
%H A381523 Emily H. Dickey and Noah A. Rosenberg, <a href="https://doi.org/10.1098/rstb.2023.0307">Labelled histories with multifurcation and simultaneity</a>, Phil. Trans. R. Soc. B 380 (2025), 20230307. (see Table 4)
%F A381523 a(n) = Y(3n+1), where Y(n) = Sum_{i=1..floor(n/4)} (n!/(i!*24^i*(n-4*i)!))*Y(n-3*i), with Y(1)=1.
%p A381523 a:= proc(n) option remember; `if`(n=0, 1, add((3*n+1)!/
%p A381523 (i!*24^i*(3*n+1-4*i)!)*a(n-i), i=1..(3*n+1)/4))
%p A381523 end:
%p A381523 seq(a(n), n=0..15); # _Alois P. Heinz_, Feb 26 2025
%Y A381523 Cf. A317059 for binary trees and A381486 for ternary trees.
%K A381523 nonn
%O A381523 0,3
%A A381523 _Noah A Rosenberg_, Feb 26 2025