The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A141268 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A141268

Number of phylogenetic rooted trees with n unlabeled objects.
(history; published version)

#31 by Susanna Cuyler at Fri May 21 04:16:16 EDT 2021

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reviewed

approved

#30 by Michel Marcus at Fri May 21 02:52:32 EDT 2021

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proposed

reviewed

#29 by Jean-François Alcover at Fri May 21 02:43:20 EDT 2021

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editing

proposed

#28 by Jean-François Alcover at Fri May 21 02:43:14 EDT 2021

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,

Sum[b[n-i*j, i-1]*Binomial[a[i]+j-1, j], {j, 0, n/i}]]];

a[n_] := If[n < 2, n, 1 + b[n, n-1]];

Array[a, 30] (* Jean-François Alcover, May 21 2021, after Alois P. Heinz *)

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approved

editing

#27 by Bruno Berselli at Thu Oct 15 03:14:40 EDT 2020

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proposed

approved

#26 by Michel Marcus at Thu Oct 15 02:45:01 EDT 2020

STATUS

editing

proposed

#25 by Michel Marcus at Thu Oct 15 02:44:57 EDT 2020

REFERENCES

Klein, Moshe, and A. Yu Khrennikov. "Recursion over partitions." P-Adic Numbers, Ultrametric Analysis, and Applications 6.4 (2014): 303-309; http://www.hamataraemet.org/wp-content/uploads/2014/10/Recursion-over-partitions-4.10.2014.pdf. (See sp_n)

LINKS

Moshe Klein and A. Yu Khrennikov, <a href="http://www.hamataraemet.org/wp-content/uploads/2014/10/Recursion-over-partitions-4.10.2014.pdf">Recursion over partitions</a, P-Adic Numbers, Ultrametric Analysis, and Applications 6.4 (2014): 303-309. See sp_n.

STATUS

approved

editing

#24 by Alois P. Heinz at Fri Oct 26 17:10:51 EDT 2018

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proposed

approved

#23 by Andrew Howroyd at Fri Oct 26 16:42:57 EDT 2018

STATUS

editing

proposed

#22 by Andrew Howroyd at Fri Oct 26 15:43:35 EDT 2018

PROG

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

seq(n)={my(v=vector(n)); for(n=1, n, v[n]=1 + EulerT(v[1..n])[n]); v} \\ Andrew Howroyd, Oct 26 2018

STATUS

approved

editing