OFFSET
1,2
COMMENTS
The weight is the number of hypertrees minus 1 plus the weight of each hyperedge which is the number of vertices it connects minus 2.
T(n,k) is also the dimension of the operad ComPreLie in arity n with k commutative products.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
FORMULA
E.g.f: series reversion in t of (log(1+x*t)/x)*exp(-t).
T(n,0) = n^(n-1).
T(n,n-1) = 1.
EXAMPLE
Triangle T(n,k) begins:
n\k 0 1 2 3 4 ...
1 1;
2 2, 1;
3 9, 9, 1;
4 64, 96, 28, 1;
5 625, 1250, 625, 75, 1;
...
PROG
(PARI) T(n) = my(x='x+O('x^(n+1))); [Vecrev(p) | p<-Vec(serlaplace( serreverse(log(1+x*y)*exp(-x)/y )))]
{my(A=T(10)); for(n=1, #A, print(A[n]))} \\ Andrew Howroyd, Oct 20 2023
CROSSREFS
KEYWORD
AUTHOR
Paul Laubie, Oct 20 2023
EXTENSIONS
a(23) corrected by Andrew Howroyd, Jan 01 2024
STATUS
approved