OFFSET
1,9
COMMENTS
See Table 2 in the Ferroni/Larson reference.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
Luis Ferroni and Matt Larson, Kazhdan-Lusztig polynomials of braid matroids, arXiv:2303.02253 [math.CO], 2023.
Nicholas Proudfoot, Yuan Xu, and Ben Young, On the enumeration of series-parallel matroids, arXiv:2406.04502 [math.CO], 2024.
FORMULA
E.g.f.: A(x,y) = B(log(1 + x), y)/(1 + x) - 1 where B(x,y) is the e.g.f. of A359985.
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 0, 5, 1;
0, 0, 15, 16, 1;
0, 0, 0, 175, 42, 1;
0, 0, 0, 735, 1225, 99, 1;
0, 0, 0, 0, 16065, 6769, 219, 1;
0, 0, 0, 0, 76545, 204400, 32830, 466, 1;
...
PROG
(PARI) \\ B gives A359985 as e.g.f.
B(n)= {exp(x*(1+y) + y*intformal(serreverse(log(1 + x*y + O(x^n))/y + log(1 + x + O(x^n)) - x)))}
T(n) = {[Vecrev(p/y) | p<-Vec(serlaplace(subst(B(n), x, log(1 + x + O(x*x^n)))/(1 + x) - 1))]}
{ my(A=T(9)); for(i=1, #A, print(A[i])) }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 09 2023
STATUS
approved