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%I #20 Sep 08 2022 08:45:32
%S 0,1,7,45,312,2400,20520,194040,2016000,22861440,281232000,3732220800,
%T 53169177600,809512704000,13120332825600,225573828480000,
%U 4100866818048000,78606921609216000
%N Number of cells in the 2nd rows 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=0..n-1} k*A134436(n,k).
%D E. Barcucci, A. del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%H Vincenzo Librandi, <a href="/A134437/b134437.txt">Table of n, a(n) for n = 1..400</a>
%F a(n) = (1/4)*(3n-2)*(n-1)*(n-1)!.
%F a(n) = (1/2)*(3n-4)*(n-1)! + (n-1)*a(n-1); a(1)=0.
%F a(n) = (n+2)!*Sum_{k=1..n} ((2*k-1)/(k*(k+1)*(k+2))). - _Gary Detlefs_, Sep 20 2011
%F D-finite with recurrence +3*a(n) +(-3*n-11)*a(n-1) +2*(4*n-3)*a(n-2) +2*(-n+3)*a(n-3)=0. - _R. J. Mathar_, Jul 26 2022
%e a(2)=1 because the horizontal domino has no cells in the 2nd row and the vertical domino has 1 cell in the 2nd row.
%p seq((1/4)*(3*n-2)*(n-1)*factorial(n-1), n = 1 .. 18)
%t Table[((3n-2)(n-1)(n-1)!)/4,{n,20}] (* _Harvey P. Dale_, Sep 23 2011 *)
%o (Magma)[(3*n-2)*(n-1)*Factorial(n-1)/4: n in [1..20]]; // _Vincenzo Librandi_, Sep 24 2011
%Y Cf. A134436.
%K nonn
%O 1,3
%A _Emeric Deutsch_, Nov 30 2007
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