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 A381866 #14 Mar 12 2025 13:13:01
%S A381866 1,1,126,162162,1003458456,20419376121144,1084881453316380720,
%T A381866 128835096988586792403600,30577206578883234961900809600,
%U A381866 13328512616115465470187677202211200,9988360697491697592427704919982668857600,12203369577406758958826880335333105520792518400
%N A381866 Number of labeled histories for rooted 5-furcating trees with 4n+1 leaves if simultaneous 5-furcations are not allowed.
%H A381866 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 1).
%F A381866 a(n) = ((4*n+1)!/120^n) * Product_{i=1..n} (4*i-3).
%F A381866 a(n) = Gamma(4*n+2)*Gamma(n+1/4)/(30^n*Gamma(1/4)). - _Stefano Spezia_, Mar 09 2025
%F A381866 a(n) = A007696(n)*(4*n+1)!/120^n. - _Alois P. Heinz_, Mar 10 2025
%t A381866 a[n_]:=((4*n+1)!/120^n)*Product[(4*i-3),{i,n}]; Array[a,11,0] (* _Stefano Spezia_, Mar 09 2025 *)
%Y A381866 Cf. A006472, A339411, A381536 for bifurcating, trifurcating, and quadfurcating trees; A381533 if simultaneity is allowed.
%Y A381866 Cf. A007696.
%K A381866 nonn
%O A381866 0,3
%A A381866 _Noah A Rosenberg_, Mar 08 2025