A372017 G.f. A(x) satisfies A(x) = ( 1 + 9*x/(1 - x*A(x)) )^(1/3).

1, 3, -6, 39, -213, 1425, -9681, 69393, -509307, 3827856, -29254443, 226787682, -1778491446, 14084085711, -112462798281, 904485811944, -7319902809228, 59565238152789, -487071807495099, 4000169922457260, -32980470088198209, 272875134913543488

Offset: 0

Author

Seiichi Manyama, Apr 15 2024

Keywords

• sign

Crossrefs

Cf. A372003.

Programs

PARI

a(n) = sum(k=0, n, 9^k*binomial(n/3-k/3+1/3, k)*binomial(n-1, n-k)/(n-k+1));

Formula

a(n) = Sum_{k=0..n} 9^k * binomial(n/3-k/3+1/3,k) * binomial(n-1,n-k)/(n-k+1).