A381536 Number of labeled histories for rooted 4-furcating trees with 3n+1 leaves if simultaneous 4-furcations are not allowed.
1, 1, 35, 7350, 5255250, 9564555000, 37072215180000, 271183254041700000, 3430468163627505000000, 70238835650273164875000000, 2210064963735845132791875000000, 102493972758213553878355995000000000, 6769214430816214165896021689775000000000, 618638506832293812621237422228537250000000000
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).
Programs
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Maple
a:= n-> (3*n+1)!/24^n*mul(3*i-2, i=1..n): seq(a(n), n=0..13); # Alois P. Heinz, Feb 26 2025
Formula
a(n) = ((3*n+1)!/24^n) * Product_{i=1..n} (3*i-2).