OFFSET
1,4
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
EXAMPLE
The a(2) = 1 through a(5) = 11 phylogenetic trees:
(12) (123) (1234) (12345)
((12)(34)) ((12)(345))
((13)(24)) ((13)(245))
((14)(23)) ((14)(235))
((15)(234))
((23)(145))
((24)(135))
((25)(134))
((34)(125))
((35)(124))
((45)(123))
MATHEMATICA
numSetPtnsOfType[ptn_]:=Total[ptn]!/Times@@Factorial/@ptn/Times@@Factorial/@Length/@Split[ptn];
rotf[n_]:=rotf[n]=If[n==1, 0, 1+Sum[numSetPtnsOfType[p]*Times@@rotf/@p, {p, Select[IntegerPartitions[n], Length[#]>1&]}]];
Array[rotf, 20]
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
b(n, k)={my(v=vector(n)); for(n=2, n, v[n]=binomial(n+k-1, n) + EulerT(v[1..n])[n]); v}
seq(n)={my(M=Mat(vectorv(n, k, b(n, k)))); vector(n, k, sum(i=1, k, binomial(k, i)*(-1)^(k-i)*M[i, k]))} \\ Andrew Howroyd, Oct 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 09 2018
STATUS
approved