A362164 Expansion of e.g.f. -exp(x * (1-3*x)^(1/3)).
-1, -1, 1, 11, 63, 499, 6089, 97551, 1875551, 41846183, 1062206289, 30214274419, 951599063711, 32864817109851, 1234766859596633, 50132215859126519, 2187063341006059839, 102022039514031274831, 5067161180856909388961, 266960634868753685833563
Offset: 0
Programs
-
Mathematica
With[{nn=20},CoefficientList[Series[-Exp[x*CubeRoot[1-3x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 18 2025 *) -
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x*(1-3*x)^(1/3))))
Formula
a(n) = - n! * Sum_{k=0..n} (-3)^k * binomial((n-k)/3,k)/(n-k)!.