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A359985 Triangle read by rows: T(n,k) is the number of quasi series-parallel matroids on [n] with rank k, 0 <= k <= n.

%I A359985 #13 Oct 15 2024 15:08:24
%S A359985 1,1,1,1,3,1,1,7,7,1,1,15,35,15,1,1,31,155,155,31,1,1,63,651,1365,651,
%T A359985 63,1,1,127,2667,10941,10941,2667,127,1,1,255,10795,82215,156597,
%U A359985 82215,10795,255,1,1,511,43435,589135,1988007,1988007,589135,43435,511,1
%N A359985 Triangle read by rows: T(n,k) is the number of quasi series-parallel matroids on [n] with rank k, 0 <= k <= n.
%C A359985 A quasi series-parallel matroid is a collection of series-parallel matroids. See the Ferroni/Larson reference for a precise definition.
%C A359985 The first six rows of this triangle are the same as A022166.
%H A359985 Andrew Howroyd, <a href="/A359985/b359985.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%H A359985 Luis Ferroni and Matt Larson, <a href="https://arxiv.org/abs/2303.02253">Kazhdan-Lusztig polynomials of braid matroids</a>, arXiv:2303.02253 [math.CO], 2023.
%H A359985 Nicholas Proudfoot, Yuan Xu, and Ben Young, <a href="https://arxiv.org/abs/2406.04502">On the enumeration of series-parallel matroids</a>, arXiv:2406.04502 [math.CO], 2024.
%e A359985 Triangle begins:
%e A359985   1;
%e A359985   1,   1;
%e A359985   1,   3,    1;
%e A359985   1,   7,    7,     1;
%e A359985   1,  15,   35,    15,     1;
%e A359985   1,  31,  155,   155,    31,    1;
%e A359985   1,  63,  651,  1365,   651,   63,   1;
%e A359985   1, 127, 2667, 10941, 10941, 2667, 127, 1;
%e A359985   ...
%o A359985 (PARI) \\ Proposition 2.3, 2.8 in Ferroni/Larson, compare A140945.
%o A359985 T(n) = {[Vecrev(p) | p<-Vec(serlaplace(exp(x*(y+1) + y*intformal( serreverse(log(1 + x*y + O(x^n))/y + log(1 + x + O(x^n)) - x)))))]}
%o A359985 { my(A=T(8)); for(i=1, #A, print(A[i])) }
%Y A359985 Row sums are A359986.
%Y A359985 Columns k=0..2 are A000012, A000225, A006095.
%Y A359985 Cf. A022166, A140945.
%K A359985 nonn,tabl
%O A359985 0,5
%A A359985 _Andrew Howroyd_, Mar 08 2023