%I
%S 1,0,2,0,0,4,2,0,0,0,8,8,6,2,0,0,0,0,16,24,28,26,16,8,2,0,0,0,0,0,32,
%T 64,96,120,126,110,82,52,26,10,2,0,0,0,0,0,0,64,160,288,432,564,658,
%U 680,638,542,416,284,172,90,38,12,2,0,0,0,0,0,0,0,128,384,800,1376,2072
%N Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and area k (n>=1, k>=1). A deco polyomino is a directed columnconvex polyomino in which the height, measured along the diagonal, is attained only in the last column.
%C Row n has 1+n(n1)/2 terms, the first n1 being 0's. Row sums are the factorials (A000142). T(n,n)=2^(n1). Sum(k*T(n,k), k=1..1+n(n1)/2)=A121553(n).
%D E. Barcucci, A. del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 2942.
%F The row generating polynomials are P(1,t)=t and P(n,t)=2t^n*product(2+t+t^2+...+t^j, j=1..n2) for n>=2.
%e Triangle starts:
%e 1;
%e 0,2;
%e 0,0,4,2;
%e 0,0,0,8,8,6,2;
%e 0,0,0,0,16,24,28,26,16,8,2;
%p for n from 1 to 8 do P[n]:=sort(expand(simplify(2*t^n*product(2+sum(t^i,i=1..j),j=1..n2)))) od: for n from 1 to 8 do seq(coeff(P[n],t,j),j=1..n*(n1)/2+1) od; # yields sequence in triangular form
%Y Cf. A000142, A121553.
%K nonn,tabf
%O 1,3
%A _Emeric Deutsch_, Aug 08 2006
