%I A121580
%S A121580 1,3,11,53,317,2237,18077,164237,1656077,18348557,221561357,2895986957,
%T A121580 40737113357,613623026957,9854521894157,168083120422157,
%U A121580 3034505335078157,57810369261862157,1159018646647078157
%N A121580 Number of cells in column 1 of all deco polyominoes of height n. A deco 
               polyomino is a directed column-convex polyomino in which the height, 
               measured along the diagonal, is attained only in the last column.
%C A121580 a(n)=Sum(k*A100822(n,k),k=1..n).
%D A121580 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations 
               and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121580 a(1)=1, a(n)=a(n-1)+(n-1)!*([1+n(n-1)/2] for n>=2.
%F A121580 a(n)=(1/2)Sum(j!,j=0..n+1) - n!. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 06 2008
%e A121580 a(2)=3 because the deco polyominoes of height 2 are the vertical and 
               horizontal dominoes, having, respectively, 2 and 1 cells in their 
               first columns.
%p A121580 a[1]:=1: for n from 2 to 22 do a[n]:=a[n-1]+(n-1)!*(1+n*(n-1)/2) od: 
               seq(a[n],n=1..22);
%Y A121580 Cf. A100822.
%Y A121580 Sequence in context: A074512 A005502 A000255 this_sequence A081367 A156171 
               A129093
%Y A121580 Adjacent sequences: A121577 A121578 A121579 this_sequence A121581 A121582 
               A121583
%K A121580 nonn
%O A121580 1,2
%A A121580 Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 09 2006