%I A102537
%S A102537 1,1,3,1,8,12,1,15,55,55,1,24,156,364,273,1,35,350,1400,2380,1428,1,48,
%T A102537 680,4080,11628,15504,7752,1,63,1197,9975,41895,92169,100947,43263,1,80,
%U A102537 1960,21560,123970,396704,708400,657800,246675,1,99,3036,42504
%N A102537 Triangle T(n,k) read by rows: 1/n * C(2n+k,k-1) * C(n,k).
%C A102537 Number of dissections of a convex (2n+2)-gon by k-1 noncrossing diagonals 
               into (2j+2)-gons, 1<=j<=n-1.
%H A102537 E. Tzanaki, <a href="http://arXiv.org/abs/math.CO/0501100">Polygon dissections...</
               a>
%e A102537 1
%e A102537 1,3
%e A102537 1,8,12
%e A102537 1,15,55,55
%e A102537 1,24,156,364,273
%e A102537 1,35,350,1400,2380,1428
%e A102537 1,48,680,4080,11628,15504,7752
%e A102537 1,63,1197,9975,41895,92169,100947,43263
%e A102537 1,80,1960,21560,123970,396704,708400,657800,246675
%Y A102537 Left-hand columns include A005563. Right-hand columns include essentially 
               A001764 and A013698. Row sums are in A003168.
%Y A102537 Sequence in context: A120236 A049760 A019146 this_sequence A131202 A067955 
               A049965
%Y A102537 Adjacent sequences: A102534 A102535 A102536 this_sequence A102538 A102539 
               A102540
%K A102537 nonn,tabl
%O A102537 1,3
%A A102537 Ralf Stephan, Jan 14 2005