A361354 Number of simple quasi series-parallel matroids on [n].

1, 1, 2, 6, 32, 218, 2060, 23054, 314242, 4897410, 87427276, 1741312444, 38482278928, 931618115860, 24554678866736, 699328394272236, 21410158708401980, 701011980397033052, 24445424273647475096, 904440666571331841992, 35386719095200164370912, 1459756349974815778252152

Offset: 1

Author

Andrew Howroyd, Mar 09 2023

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Luis Ferroni and Matt Larson, Kazhdan-Lusztig polynomials of braid matroids, arXiv:2303.02253 [math.CO], 2023.

Crossrefs

Row sums of A361353.

Cf. A007834, A359986.

Programs

PARI

seq(n) = Vec(serlaplace( -1 + subst(exp(2*x + intformal(-x + 2*serreverse(1 + 2*x - exp(x + O(x^n))))), x, log(1 + x + O(x*x^n)))/(1 + x) ))

Formula

E.g.f.: B(1 + log(x))/(1 + x) - 1 where B(x) is the e.g.f. of A359986.

E.g.f.: exp(B(x)) where B(x) is the e.g.f. of A007834.