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A339835 Number of rooted bicolored trees on n unlabeled nodes such that every white node is adjacent to a black node. 5
1, 3, 9, 30, 111, 424, 1705, 7024, 29692, 127748, 558219, 2469403, 11039992, 49796803, 226348740, 1035750855, 4767429667, 22058219466, 102534463563, 478602668159, 2242383155726, 10541976883286, 49714185649417, 235109360767014, 1114782699692044, 5298494249055391 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
EXAMPLE
a(1) = 1: B.
a(2) = 4: B(B), B(W), W(B).
a(3) = 9: B(BB), B(BW), B(WW), W(BB), B(B(B)), B(B(W)), B(W(B)), W(B(B)), W(B(W)).
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(u+v+w)); v=concat([0], t2-t1); w=concat([1], t1)); u+v}
CROSSREFS
Cf. A038055 (rooted bicolored trees), A339831, A339834 (unrooted), A339838.
Sequence in context: A151472 A107379 A117428 * A134168 A124427 A350589
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 19 2020
STATUS
approved

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Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)