A361355 - OEIS

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

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OFFSET

1,13

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) = log(1 + B(x,y)) where B(x,y) is the e.g.f. of A361353.

E.g.f.: A(x,y) = log(B(log(1 + x), y)/(1 + x)) where B(x,y) is the e.g.f. of A359985.

T(2*n+1, n+1) = A034941(n).

T(2*n, n+1) = A361282(n).