A367753 Number of shapes of labeled forest of rooted hypertrees with n vertices.

1, 2, 8, 55, 507, 5969, 85605, 1445420, 28110615, 618760615, 15207174501, 412790636977, 12265337498000, 395962288858946, 13800754780797740, 516494067220932259, 20658199248901273576, 879406216174705907137, 39698270229941320201019, 1894212537494300993244732

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..20.

Formula

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

Prog

(SageMath) R.<t>=PowerSeriesRing(QQ, 30); (1+t)*(ln(1+ln(1+t))*exp(-t)).reverse().egf_to_ogf().list()[1:]
(PARI) my(x='x+O('x^30)); Vec(serlaplace(serreverse((1+x)*log(1+log(1+x))*exp(-x)))) \\ Michel Marcus, Nov 30 2023

Crossrefs

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

Sequence in context: A005440 A183282 A139016 * A377098 A380020 A134954

Adjacent sequences: A367750 A367751 A367752 * A367754 A367755 A367756

Keyword

nonn

Author

Paul Laubie, Nov 29 2023

Status

approved