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 A320289 Number of phylogenetic trees with n labels and no singleton leaves. 5
 0, 1, 1, 4, 11, 86, 477, 4810, 40679, 496522, 5662933, 81759910, 1169640551, 19622623190, 336215135973, 6455705990674, 128445712218263, 2785761076726066, 62980942321570981, 1525318051255683598, 38566041706375722071, 1032726237783455193662 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000311, A000669, A002865, A005804, A141268, A300660, A304966, A304967, A319312, A320294, A320295. Sequence in context: A181275 A000850 A004796 * A298858 A181267 A280036 Adjacent sequences:  A320286 A320287 A320288 * A320290 A320291 A320292 KEYWORD nonn AUTHOR Gus Wiseman, Oct 09 2018 STATUS approved

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Last modified April 13 03:43 EDT 2021. Contains 342934 sequences. (Running on oeis4.)