A366434 G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^2.

1, 1, -4, 16, -84, 496, -3140, 20832, -142932, 1005856, -7220100, 52657392, -389088084, 2906551440, -21914464708, 166548194240, -1274531623764, 9812792232768, -75955668337412, 590742300208848, -4614140648464980, 36178872976542768, -284664427193774916

Offset: 0

Author

Seiichi Manyama, Oct 09 2023

Keywords

• sign

Crossrefs

Partial sums give A366364.

Cf. A366431, A366432, A366433, A366435, A366436, A366437.

Programs

PARI

a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(2*k, n-k)/(3*k-1));

Formula

a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(3*k-1,k) * binomial(2*k,n-k) / (3*k-1).