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A030980 Number of planted noncrossing bushes with n nodes; i.e., rooted noncrossing trees with n nodes, root degree 1 and no nonroot nodes of degree 1. 1
1, 0, 3, 4, 23, 66, 280, 1030, 4207, 16852, 69747, 289950, 1222540, 5192344, 22239672, 95864902, 415730735, 1812177000, 7936353049, 34901789568, 154067755503, 682428824890, 3032173906692, 13510960371744 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_{k=1..n} ((-1)^(n-k)*2^(n-k)*binomial(n, k)*binomial(3*k-2, k-1))/n.
G.f.: A(z) satisfies A(z)^3 + 2z*A(z)^3 - 2A(z)^2 - 4z*A(z)^2 + A(z) + 2z*A - z = 0.
D-finite with recurrence -2*n*(2*n-1)*a(n) +3*n*(n-2)*a(n-1) +30*(2*n-3)*(n-2)*a(n-2) +76*(n-2)*(n-3)*a(n-3)=0. - R. J. Mathar, Jul 24 2022
PROG
(PARI) a(n) = sum(k=1, n, ((-1)^(n-k)*2^(n-k)*binomial(n, k)*binomial(3*k-2, k-1))/n) \\ Michel Marcus, Aug 03 2017
CROSSREFS
Sequence in context: A002351 A042035 A343402 * A041861 A042377 A276815
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)