A367044 G.f. satisfies A(x) = 1 - x^2 + x*A(x)^3.

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

Links

Table of n, a(n) for n=0..24.

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. A025262, A367045.

Cf. A367040.

Sequence in context: A370479 A038112 A268039 * A235596 A346577 A367242

Adjacent sequences: A367041 A367042 A367043 * A367045 A367046 A367047

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2023

Status

approved