A362159 Expansion of e.g.f. -exp(x * (1-9*x)^(1/3)).

-1, -1, 5, 71, 1223, 34619, 1350629, 65717315, 3812715311, 256504939703, 19615931258309, 1679703910478879, 159161100818585975, 16530378160682622131, 1867052905777649782373, 227820142193907368696219, 29863924388750996422840799, 4185177460305652712999777135

Offset: 0

Author

Seiichi Manyama, Apr 10 2023

Keywords

• sign
• easy

Crossrefs

Cf. A362157.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x*(1-9*x)^(1/3))))

Formula

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