A058575 The sequence S defined in A058562.

0, 0, 1, 7, 81, 1311, 27273, 693351, 20830113, 722035503, 28364200569, 1245313236663, 60429110073489, 3211572892464639, 185523138537151977, 11574425593731913479, 775591270444009771137, 55555665263291738684367, 4236182199641241492147801

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: -(1/2)*LambertW(-2/3*exp(-2/3 + 1/3*x)) - 1/3 - x/3. - Vladeta Jovovic, Jun 25 2007

a(n) ~ sqrt(log(3/2)-1/3) * n^(n-1) / (2 * exp(n) * (log(27/8)-1)^n). - Vaclav Kotesovec, Jul 09 2013

Maple

spec := [ S, {N=Union(Z, S, P, Q), S=Set(Union(Z, P, Q), card>=2), P=Set(Union(Z, S, Q), card>=2), Q=Set(Union(Z, S, P), card>=2)}, labeled ]; [seq(combstruct[count](spec, size=n), n=0..40)]; # N=A058562, S=A058575
spec:=[S, {S=Set(Union(Z, S, S), card>=2)}, labeled]; [seq(combstruct[count](spec, size=n), n=0..20)]; # Vladeta Jovovic, Jun 25 2007

Mathematica

max = 18; se = Series[ -1/2*ProductLog[ -2/3*Exp[-2/3 + 1/3*x]] - 1/3 - x/3 , {x, 0, max}]; Join[{0, 0}, (CoefficientList[se, x] // DeleteCases[#, 0] &) ]* Range[0, max]! (* Jean-François Alcover, Jun 24 2013, after Vladeta Jovovic *)

Crossrefs

Cf. A058562.

Sequence in context: A112119 A369024 A371027 * A355220 A285062 A253265

Adjacent sequences: A058572 A058573 A058574 * A058576 A058577 A058578

Keyword

nonn

Author

N. J. A. Sloane, Dec 26 2000

Status

approved