%I #5 Jul 26 2022 11:37:04
%S 1,3,11,53,317,2237,18077,164237,1656077,18348557,221561357,
%T 2895986957,40737113357,613623026957,9854521894157,168083120422157,
%U 3034505335078157,57810369261862157,1159018646647078157
%N 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 a(n)=Sum(k*A100822(n,k),k=1..n).
%D E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F a(1)=1, a(n)=a(n-1)+(n-1)!*([1+n(n-1)/2] for n>=2.
%F a(n)=(1/2)Sum(j!,j=0..n+1) - n!. - _Emeric Deutsch_, Apr 06 2008
%F Conjecture D-finite with recurrence a(n) +(-n-4)*a(n-1) +3*(n+1)*a(n-2) +2*(-2*n+3)*a(n-3) +2*(n-3)*a(n-4)=0. - _R. J. Mathar_, Jul 26 2022
%e 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 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 Cf. A100822.
%K nonn
%O 1,2
%A _Emeric Deutsch_, Aug 09 2006
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