OFFSET
2,2
COMMENTS
The number of vertices is n-k.
Column k is a polynomial of degree 3*k. This is because adding a face can increase the number of vertices whose degree is greater than two by at most two.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..1276
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259, Table VIc.
FORMULA
T(n,n-k) = T(n,k).
EXAMPLE
Triangle begins:
1;
4, 4;
10, 47, 10;
20, 240, 240, 20;
35, 831, 2246, 831, 35;
56, 2282, 12656, 12656, 2282, 56;
84, 5362, 52164, 109075, 52164, 5362, 84;
120, 11256, 173776, 648792, 648792, 173776, 11256, 120;
...
PROG
(PARI) \\ Needs F from A342989.
G(n, m, y, z)={my(p=F(n, m, y, z)); subst(p, x, serreverse(x*p^2))}
H(n, g=1)={my(q=G(n, g, 'y, 'z)-x*(1+'z), v=Vec(polcoef(sqrt(serreverse(x/q^2)/x), g, 'y))); [Vecrev(t) | t<-v]}
{ my(T=H(10)); for(n=1, #T, print(T[n])) }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 04 2021
STATUS
approved