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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 Andrew Howroyd, Table of n, a(n) for n = 1..500 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 Adjacent sequences: A339832 A339833 A339834 * A339836 A339837 A339838 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.)