A381866 Number of labeled histories for rooted 5-furcating trees with 4n+1 leaves if simultaneous 5-furcations are not allowed.
1, 1, 126, 162162, 1003458456, 20419376121144, 1084881453316380720, 128835096988586792403600, 30577206578883234961900809600, 13328512616115465470187677202211200, 9988360697491697592427704919982668857600, 12203369577406758958826880335333105520792518400
Offset: 0
Keywords
Links
- Emily H. Dickey and Noah A. Rosenberg, Labelled histories with multifurcation and simultaneity, Phil. Trans. R. Soc. B 380 (2025), 20230307 (see Table 1).
Crossrefs
Programs
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Mathematica
a[n_]:=((4*n+1)!/120^n)*Product[(4*i-3),{i,n}]; Array[a,11,0] (* Stefano Spezia, Mar 09 2025 *)
Formula
a(n) = ((4*n+1)!/120^n) * Product_{i=1..n} (4*i-3).
a(n) = Gamma(4*n+2)*Gamma(n+1/4)/(30^n*Gamma(1/4)). - Stefano Spezia, Mar 09 2025
a(n) = A007696(n)*(4*n+1)!/120^n. - Alois P. Heinz, Mar 10 2025