A361353 Triangle read by rows: T(n,k) is the number of simple quasi series-parallel matroids on [n] with rank k, 1 <= k <= n.
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, 0, 0, 0, 0, 0, 2747745, 2001230, 147466, 968, 1, 0, 0, 0, 0, 0, 13835745, 56143395, 16813720, 632434, 1981, 1
Offset: 1
Examples
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; ...
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
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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])) }
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.
Comments