A366436 G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^3.

1, 1, -6, 36, -272, 2304, -20880, 198080, -1942080, 19521792, -200101376, 2083538688, -21976624128, 234321952768, -2521446660096, 27347192389632, -298643542716416, 3280990949720064, -36238161907974144, 402146115064233984, -4481721683926056960

Offset: 0

Author

Seiichi Manyama, Oct 09 2023

Keywords

• sign

Crossrefs

Partial sums give A366365.

Cf. A366431, A366432, A366433, A366434, A366435, A366437.

Programs

PARI

a(n) = (-1)^(n-1)*sum(k=0, n, binomial(4*k-1, k)*binomial(3*k, n-k)/(4*k-1));

Formula

a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(4*k-1,k) * binomial(3*k,n-k) / (4*k-1).