OFFSET
1,3
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))(3):
seq(a(n), n=1..30); # Alois P. Heinz, Sep 07 2019
MATHEMATICA
b[n_, k_] := b[n, k] = If[n < 2, k n, If[OddQ[n], 0, Function[t, t(1 - t)/2 ][b[n/2, k]]] + Sum[b[i, k] b[n - i, k], {i, 1, n/2}]];
a[n_] := Function[k, Sum[(-1)^i Binomial[k, i] b[n, k - i], {i, 0, k}]][3];
Array[a, 30] (* Jean-François Alcover, Apr 08 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 22 2012
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Sep 23 2018
STATUS
approved