A220817 Number of rooted binary MUL-trees with n leaves on the label set [4].

4, 10, 40, 215, 1260, 8010, 53240, 366680, 2590420, 18674660, 136809240, 1015603015, 7622900360, 57753364510, 441081947840, 3392237023425, 26248421645200, 204202630151860, 1596256637347240, 12531697773337965, 98763817012822460, 781102051887068160

Offset: 1

Author

N. J. A. Sloane, Dec 22 2012

Keywords

• nonn

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.

Crossrefs

Column k=4 of A319539.

Programs

Mathematica

a[n_] := a[n] = If[n < 2, 4 n, If[OddQ[n], 0, (# (1 - #)/2 &)[a[n/2]]] + Sum[a[i] a[n - i], {i, 1, n/2}]];
Array[a, 25] (* Jean-François Alcover, Sep 02 2019, after Alois P. Heinz in A319539 *)

Extensions

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