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

1,2

Links

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

Prog

(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}

Crossrefs

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

Sequence in context: A002459 A216434 A220829 * A104383 A205480 A108523

Adjacent sequences: A339835 A339836 A339837 * A339839 A339840 A339841

Keyword

nonn

Author

Andrew Howroyd, Dec 20 2020

Status

approved