A360988 E.g.f. A(x) satisfies A(x) = exp(x * A(-x)^3).

1, 1, -5, -44, 829, 14656, -488897, -13063616, 629051449, 22531502080, -1420908901469, -63859764079616, 4983153798630709, 269501734545522688, -25073583375908431769, -1585437525801020801024, 171326697778165116452977, 12401692280007001315999744

Offset: 0

Author

Seiichi Manyama, Feb 27 2023

Keywords

• sign

Crossrefs

Cf. A141369, A196198, A360987, A360989, A360990.

Cf. A168601.

Programs

PARI

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

Formula

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

a(0) = 1; a(n) = (-1)^(n-1) * (n-1)! * Sum_{i, j, k, l>=0 and i+j+k+l=n-1} (-1)^i * (n-i) * a(i) * a(j) * a(k) * a(l)/(i! * j! * k! * l!). - Seiichi Manyama, Jul 06 2025