A367753 - OEIS

%I #19 Dec 17 2023 10:27:10

%S 1,2,8,55,507,5969,85605,1445420,28110615,618760615,15207174501,

%T 412790636977,12265337498000,395962288858946,13800754780797740,

%U 516494067220932259,20658199248901273576,879406216174705907137,39698270229941320201019,1894212537494300993244732

%N Number of shapes of labeled forest of rooted hypertrees with n vertices.

%C See A367752 for the definition of the shape of a labeled rooted hypertree.

%F E.g.f.: series reversion of (1+x)*log(1+log(1+x))*exp(-x).

%o (SageMath) R.<t>=PowerSeriesRing(QQ,30);(1+t)*(ln(1+ln(1+t))*exp(-t)).reverse().egf_to_ogf().list()[1:]

%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(serreverse((1+x)*log(1+log(1+x))*exp(-x)))) \\ _Michel Marcus_, Nov 30 2023

%Y Cf. A052888, A210586, A364709, A364816, A367752.

%K nonn

%O 1,2

%A _Paul Laubie_, Nov 29 2023