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 A381533 #8 Mar 08 2025 20:48:57
%S A381533 1,1,126,198198,1552358808,41269930621920,2917021792126858416,
%T A381533 466738566750935966462976,150642168106131265276308435840,
%U A381533 89930728809765858827345682838905216,92814015425659158860323886440105229380608,156870775305420194841270876582071899442900414976,415352074564676036635314305973768435826840253066044416
%N A381533 Number of labeled histories for rooted 5-furcating trees with 4n+1 leaves if simultaneous 5-furcations are allowed.
%H A381533 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 A381533 a(n) = Y(4n+1), where Y(n) = Sum_{i=1..floor(n/5)} (n!/(i!*120^i*(n-5*i)!)) * Y(n-4*i), with Y(1)=1.
%p A381533 a:= proc(n) option remember; `if`(n=0, 1, add((4*n+1)!/
%p A381533 (i!*120^i*(4*n+1-5*i)!)*a(n-i), i=1..(4*n+1)/5))
%p A381533 end:
%p A381533 seq(a(n), n=0..12); # _Alois P. Heinz_, Feb 26 2025
%Y A381533 Cf. A317059, A381486, A381523.
%K A381533 nonn
%O A381533 0,3
%A A381533 _Noah A Rosenberg_, Feb 26 2025