A339838 Number of rooted bicolored trees on n unlabeled nodes such that black nodes are not adjacent to each other and every white node is adjacent to a black node.

1, 2, 4, 10, 27, 75, 221, 662, 2042, 6402, 20407, 65828, 214720, 706600, 2343767, 7826752, 26293468, 88796471, 301290197, 1026595232, 3511246069, 12050780294, 41488523002, 143246116231, 495881545520, 1720771421470, 5984652387281, 20857113949868, 72829214554641, 254762923125929

Offset: 1

Author

Andrew Howroyd, Dec 20 2020

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A038055 (rooted bicolored trees), A339831, A339835, A339837.

Programs

PARI

EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
seq(n)={my(u=v=w=[]); for(n=1, n, my(t1=EulerT(v), t2=EulerT(u+v)); u=concat([1], EulerT(v+w)); v=concat([0], t2-t1); w=concat([1], t1)); u+v}