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.
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
KEYWORD
nonn,easy
AUTHOR
Paul Laubie, Oct 21 2023
STATUS
approved