This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A131635 #7 Nov 21 2013 12:49:05
%S A131635 1,3,18,6,60,300,10,150,1050,4900,15,315,2940,17640,79380,21,588,7056,
%T A131635 52920,291060,1280664,28,1008,15120,138600,914760,4756752,20612592,36,
%U A131635 1620,29700,326700,2548260,15459444,77297220,331273800,45,2475,54450
%N A131635 Triangle T(n,m)=m*n*binomial(m+n,m)^2/(2*(m+n)) read by rows.
%C A131635 First two columns are essentially A000217 and A006011.
%H A131635 V. J. W. Guo and J. Zeng, <a href="http://dx.doi.org/10.1016/j.cam.2004.11.009">A note on two identities arising from enumeration of convex polyominoes</a>, J. Comp. Appl. Math. 180 (2005) pp 413-423.
%F A131635 T(n,m)=m*n*A000290(A007318(n+m,m))/[2(m+n)].
%e A131635 Triangle is symmetric in the two indices and starts
%e A131635 1,
%e A131635 3, 18,
%e A131635 6, 60, 300,
%e A131635 10, 150, 1050, 4900,
%e A131635 15, 315, 2940, 17640, 79380,
%e A131635 21, 588, 7056, 52920, 291060, 1280664,
%p A131635 a := proc(n,m) m*n*(binomial(m+n,n))^2/2/(m+n) ; end: for n from 1 to 10 do for m from 1 to n do printf("%d, ",a(n,m)) ; od: od:
%t A131635 Flatten[Table[m*n*Binomial[m+n,m]^2/(2(m+n)),{n,10},{m,n}]] (* _Harvey P. Dale_, Dec 24 2011 *)
%o A131635 (PARI) A131635(n,m) = m*n*binomial(m+n,m)^2/(2*(m+n))
%K A131635 easy,nonn,tabl
%O A131635 1,2
%A A131635 _R. J. Mathar_, Sep 05 2007