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

0,4

Links

Table of n, a(n) for n=0..19.

Formula

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

Mathematica

With[{nn=20}, CoefficientList[Series[-Exp[x*CubeRoot[1-3x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 18 2025 *)

Prog

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

Crossrefs

Cf. A362159, A362177.

Sequence in context: A053367 A163706 A180763 * A357959 A285361 A237358

Adjacent sequences: A362161 A362162 A362163 * A362165 A362166 A362167

Keyword

sign,easy

Author

Seiichi Manyama, Apr 10 2023

Status

approved