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A100728 Number of rank-(n-2) simple matroids on S_n. 1

%I #15 Oct 10 2019 04:24:22

%S 1,31,337,2570,16865,104858,650761,4145956,27483392,190522216,

%T 1382087111,10478149999,82860356456,682066659044,5832719543338,

%U 51724107920729,474869705028520,4506715494154371,44152005320340946

%N Number of rank-(n-2) simple matroids on S_n.

%H W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/matroid.html">Tables of matroids</a>.

%H W. M. B. Dukes, <a href="https://web.archive.org/web/20030208144026/http://www.stp.dias.ie/~dukes/phd.html">Counting and Probability in Matroid Theory</a>, Ph.D. Thesis, Trinity College, Dublin, 2000.

%H W. M. B. Dukes, <a href="https://arxiv.org/abs/math/0411557">The number of matroids on a finite set</a>, arXiv:math/0411557 [math.CO], 2004. [See Lemma 2.2(iii).]

%H W. M. B. Dukes, <a href="http://emis.impa.br/EMIS/journals/SLC/wpapers/s51dukes.html">On the number of matroids on a finite set</a>, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g. [See Lemma 2.2(iii).]

%F a(n) = Bell(n+1) - (n^2+n+4)*2^(n-2) + n*(n+1)*(3*n^2-n+10)/24.

%Y Cf. A000110 (Bell numbers). Diagonal of A058720.

%K nonn

%O 4,2

%A _Ralf Stephan_, Nov 29 2004

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)