%I A058716
%S A058716 1,0,1,0,1,1,0,1,2,1,0,1,4,3,1,0,1,6,9,4,1,0,1,10,25,18,5,1,0,1,14,
%T A058716 70,85,31,6,1,0,1,21,217,832,288,51,7,1
%N A058716 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank 
               k on n labeled points (n >= 0, 0<=k<=n).
%C A058716 A signed version is given by A119328. - Paul Barry (pbarry(AT)wit.ie), 
               May 14 2006
%H A058716 W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/matroid.html">
               Tables of matroids</a>
%H A058716 W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/phd.html">Counting 
               and Probability in Matroid Theory</a>, Ph.D. Thesis, Trinity College, 
               Dublin, 2000.
%H A058716 <a href="Sindx_Mat.html#matroid">Index entries for sequences related 
               to matroids</a>
%F A058716 T(n,k)=sum{i=0..n, (-1)^(i-k)*C(n,i)*sum{j=0..i-k, C(k,2j)*C(i-k,2j)}}; 
               Column k has g.f. (x/(1-x))^k*sum{j=0..k, C(k,2j)x^(2j)}. - Paul 
               Barry (pbarry(AT)wit.ie), May 14 2006
%e A058716 1; 0,1; 0,1,1; 0,1,2,1; 0,1,4,3,1; ...
%Y A058716 Cf. A058717 (same except for border), A058710, A058711. Row sums give 
               A058718. Diagonals give A000065, A058719.
%Y A058716 Sequence in context: A055277 A055340 A119328 this_sequence A048723 A088455 
               A004248
%Y A058716 Adjacent sequences: A058713 A058714 A058715 this_sequence A058717 A058718 
               A058719
%K A058716 nonn,tabl,nice
%O A058716 0,9
%A A058716 N. J. A. Sloane (njas(AT)research.att.com), Dec 31 2000