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A220824

Number of rooted gene trees with n leaves on the label set [4].

4, 10, 60, 430, 3396, 28818, 256172, 2357138, 22253672, 214370398, 2098593628, 20817790876, 208801698676, 2113957366698, 21574762692484, 221729081428478, 2292720460828372, 23835381083324608, 248987501825970604, 2612160344953154508, 27510833867426222908

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OFFSET

1,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

V. P. Johnson, Enumeration Results on Leaf Labeled Trees, Ph. D. Dissertation, Univ. Southern Calif., 2012.

MATHEMATICA

A[n_, k_] := A[n, k] = If[n < 2, k n, If[OddQ[n], 0, (# (1 - #)/2)&[A[n/2, k]]] + Sum[A[i, k] A[n - i, k], {i, 1, n/2}]];

T[n_, k_] := Sum[(-1)^i Binomial[k, i] A[n, k - i], {i, 0, k}];

a[n_] := T[n, 5];

Array[a, 22] (* Jean-François Alcover, Sep 02 2019, after Alois P. Heinz in A319254 *)

CROSSREFS