A361355 Triangle read by rows: T(n,k) is the number of simple series-parallel matroids on [n] with rank k, 1 <= k <= n.
1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 15, 1, 0, 0, 0, 0, 75, 1, 0, 0, 0, 0, 735, 280, 1, 0, 0, 0, 0, 0, 9345, 938, 1, 0, 0, 0, 0, 0, 76545, 77805, 2989, 1, 0, 0, 0, 0, 0, 0, 1865745, 536725, 9285, 1, 0, 0, 0, 0, 0, 0, 13835745, 27754650, 3334870, 28446, 1, 0
Offset: 1
Examples
Triangle begins: 1; 0, 0; 0, 1, 0; 0, 0, 1, 0; 0, 0, 15, 1, 0; 0, 0, 0, 75, 1, 0; 0, 0, 0, 735, 280, 1, 0; 0, 0, 0, 0, 9345, 938, 1, 0; 0, 0, 0, 0, 76545, 77805, 2989, 1, 0; ...
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.
Programs
-
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) = {my(v=Vec(serlaplace(log(subst(B(n), x, log(1 + x + O(x*x^n)))/(1 + x))))); vector(#v, n, Vecrev(v[n]/y, n))} { my(A=T(9)); for(i=1, #A, print(A[i])) }