Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Mar 17 2015 15:52:29
%S 1,1,1,1,1,2,4,2,1,1,3,10,12,10,3,1,1,4,21,49,78,49,21,4,1,1,5,39,172,
%T 584,778,584,172,39,5,1,1,6,68,573,5236,18033,46661,18033,5236,573,68,
%U 6,1,1,7,112,1890,72205,971573,149636721,19498369,149636721,971573,72205,1890,112,7,1
%N Triangular array of numbers of 2-polymatroids of rank k on n unlabeled points, for n>=0, 0<=k<=2n.
%C The rows are symmetric: a(n,k) = a(n,2n-k).
%C Starting with n=7, the rows are not unimodal.
%H Thomas J. Savitsky, <a href="http://epubs.siam.org/doi/abs/10.1137/140955094">Enumeration of 2-polymatroids on up to seven elements</a>. SIAM J. Discrete Math., 28(4):1641-1650, 2014. <a href="http://arxiv.org/abs/1401.8006">arXiv:1401.8006</a>
%e Triangle starts with:
%e n=0: 1
%e n=1: 1 1 1
%e n=2: 1 2 4 2 1
%e n=3: 1 3 10 12 10 3 1
%e n=4: 1 4 21 49 78 49 21 4 1
%e n=5: 1 5 39 172 584 778 584 172 39 5 1
%e n=6: 1 6 68 573 5236 18033 46661 18033 5236 573 68 6 1
%e n=7: 1 7 112 1890 72205 971573 149636721 19498369 149636721 971573 72205 1890 112 7 1
%Y Cf. A256157, A256158, A256159, A053534
%K nonn,tabf
%O 0,6
%A _Max Alekseyev_, Mar 16 2015