A364816 Number of labeled forests of rooted Greg hypertrees with n white vertices.

1, 4, 38, 587, 12607, 347158, 11668113, 463118041, 21199488803, 1099465138203, 63715991036964, 4080500855334901, 286178278238641752, 21813909692571410084, 1795659553423061982001, 158754024731440581761116, 15002712207593790179795284, 1509215071938528737864389367, 161017605699030302902310357883

Offset

1,2

Comments

A Greg hypertree is a hypertree with black and white vertices, such that black vertices are unlabeled and have at least two incoming edges.

Links

Table of n, a(n) for n=1..19.

Formula

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

a(n) ~ sqrt((1+s)*(2+s)/((1+r)*(3 + s*(3+s)))) * n^(n-1) / (exp(n) * r^(n - 1/2)), where s = 0.3900539630495916058133890253422601894372373496844... is the root of the equation exp(-s + 1/(1+s)) = 1+s and r = exp(-s)*(1 + 1/(1+s)) - 1 = 0.1640664235584946357534702598223332293549130374395... - Vaclav Kotesovec, Oct 24 2023

Mathematica

Rest[CoefficientList[InverseSeries[Series[E^-x (1 + x + Log[1 + x]) - 1, {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Oct 24 2023 *)

Prog

(PARI) my(t='t+O('t^25)); Vec(serlaplace(serreverse((log(1+t)-exp(t)+t+1)*exp(-t)))) \\ Michel Marcus, Oct 21 2023

Crossrefs

Cf. A005264, A052888.

Sequence in context: A113664 A217900 A077745 * A277869 A138214 A195442

Adjacent sequences: A364813 A364814 A364815 * A364817 A364818 A364819

Keyword

nonn,easy

Author

Paul Laubie, Oct 21 2023

Status

approved