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A367044
G.f. satisfies A(x) = 1 - x^2 + x*A(x)^3.
1
1, 1, 2, 9, 40, 192, 963, 5000, 26649, 144990, 802023, 4497150, 25504380, 146037955, 843134220, 4902661503, 28686940053, 168785282241, 997968554037, 5926617173205, 35335723342962, 211433954924955, 1269252184538408, 7642065274626855, 46137678521488140
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*(n-2*k)+1,k) * binomial(3*(n-2*k),n-2*k)/(2*(n-2*k)+1).
PROG
(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(2*(n-2*k)+1, k)*binomial(3*(n-2*k), n-2*k)/(2*(n-2*k)+1));
CROSSREFS
Cf. A367040.
Sequence in context: A370479 A038112 A268039 * A235596 A346577 A367242
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 03 2023
STATUS
approved