A220821 Number of rooted binary leaf-multilabeled trees with n leaves on the label set [4].

0, 0, 0, 15, 240, 2604, 24180, 207732, 1710108, 13739550, 108853512, 855732465, 6700902804, 52395480996, 409733313444, 3207687963129, 25155951725808, 197703130100532, 1557413160706764, 12298597436673711, 97359729090421320, 772615510913274126, 6145842794363133324

Offset

1,4

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.

Maple

b:= proc(n, k) option remember; `if`(n<2, k*n, `if`(n::odd, 0,
      (t-> t*(1-t)/2)(b(n/2, k)))+add(b(i, k)*b(n-i, k), i=1..n/2))
    end:
a:= n-> (k-> add((-1)^i*binomial(k, i)*b(n, k-i), i=0..k))(4):
seq(a(n), n=1..30);  # Alois P. Heinz, Sep 07 2019

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, 4];
Array[a, 23] (* Jean-François Alcover, Sep 02 2019, after Alois P. Heinz in A319541 *)

Crossrefs

Column k=4 of A319541.

Sequence in context: A343527 A097262 A158557 * A090411 A154806 A133199

Adjacent sequences: A220818 A220819 A220820 * A220822 A220823 A220824

Keyword

nonn

Author

N. J. A. Sloane, Dec 22 2012

Extensions

Terms a(11) and beyond from Andrew Howroyd, Sep 23 2018

Status

approved