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

1, 31, 337, 2570, 16865, 104858, 650761, 4145956, 27483392, 190522216, 1382087111, 10478149999, 82860356456, 682066659044, 5832719543338, 51724107920729, 474869705028520, 4506715494154371, 44152005320340946

Offset: 4

Author

Ralf Stephan, Nov 29 2004

Keywords

• nonn

Links

• W. M. B. Dukes, Tables of matroids.
• W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.
• W. M. B. Dukes, The number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004. [See Lemma 2.2(iii).]
• W. M. B. Dukes, On the number of matroids on a finite set, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g. [See Lemma 2.2(iii).]

Crossrefs

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

Formula

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