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A100728
Number of rank-(n-2) simple matroids on S_n.
1
1, 31, 337, 2570, 16865, 104858, 650761, 4145956, 27483392, 190522216, 1382087111, 10478149999, 82860356456, 682066659044, 5832719543338, 51724107920729, 474869705028520, 4506715494154371, 44152005320340946
OFFSET
4,2
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).]
FORMULA
a(n) = Bell(n+1) - (n^2+n+4)*2^(n-2) + n*(n+1)*(3*n^2-n+10)/24.
CROSSREFS
Cf. A000110 (Bell numbers). Diagonal of A058720.
Sequence in context: A123568 A111675 A142495 * A332945 A296730 A274180
KEYWORD
nonn
AUTHOR
Ralf Stephan, Nov 29 2004
STATUS
approved