OFFSET
0,6
COMMENTS
See section 2 of the Labelle reference.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325
G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees, arXiv:math/0312424 [math.CO], Dec 23 2003.
FORMULA
Column k is the Euler transform of column k+1 of A242249.
G.f. of column k: A(x) satisfies A(x) = exp(Sum_{i>0} x^i*A(x^i)^(k-1)/i).
EXAMPLE
Array begins:
============================================================
n\k | 2 3 4 5 6 7 8
----+-------------------------------------------------------
0 | 1 1 1 1 1 1 1 ...
1 | 1 1 1 1 1 1 1 ...
2 | 2 3 4 5 6 7 8 ...
3 | 4 10 19 31 46 64 85 ...
4 | 9 39 107 229 421 699 1079 ...
5 | 20 160 647 1832 4191 8325 14960 ...
6 | 48 702 4167 15583 44322 105284 220193 ...
7 | 115 3177 27847 137791 487662 1385888 3374267 ...
8 | 286 14830 191747 1255202 5527722 18795035 53275581 ...
...
PROG
(PARI) \\ here B(n, k) gives g.f. of k-th column.
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
B(n, k)={my(p=1+O(x)); for(n=1, n, p=1+x*Ser(EulerT(Vec(p^(k-1))))); p}
{ Mat(vector(7, k, Col(B(7, k+1)))) }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 02 2021
STATUS
approved