%I #26 Jul 26 2022 14:06:30

%S 1,1,2,8,42,264,1920,15840,146160,1491840,16692480,203212800,

%T 2674425600,37841126400,572885913600,9240898867200,158228598528000,

%U 2866422214656000,54775863926784000,1101208277385216000,23234214178086912000,513342323725271040000

%N Number of deco polyominoes of height n, having no 2-cell columns starting at level 0. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.

%H Alois P. Heinz, <a href="/A121635/b121635.txt">Table of n, a(n) for n = 1..450</a> (n=2..101 from Muniru A Asiru)

%H E. Barcucci, A. Del Lungo and R. Pinzani, <a href="http://dx.doi.org/10.1016/0304-3975(95)00199-9">"Deco" polyominoes, permutations and random generation</a>, Theoretical Computer Science, 159, 1996, 29-42.

%H Mark Dukes, Chris D White, <a href="http://arxiv.org/abs/1603.01589">Web Matrices: Structural Properties and Generating Combinatorial Identities</a>, arXiv:1603.01589 [math.CO], 2016.

%H Mark Dukes, Chris D. White, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i1p45">Web Matrices: Structural Properties and Generating Combinatorial Identities</a>, Electronic Journal Of Combinatorics, 23(1) (2016), #P1.45.

%F a(n) = A121634(n,0).

%F a(1)=1, a(n) = (n-2)!(n^2-3*n+4)/2 = A000142(n-2)*A152947(n) for n>=2.

%F a(1)=1, a(2)=1, a(n) = (n-2)*[(n-2)! + a(n-1)] for n>=3.

%F D-finite with recurrence a(n) +(-n-2)*a(n-1) +2*(n-1)*a(n-2) +2*(-n+4)*a(n-3)=0. - _R. J. Mathar_, Jul 26 2022

%e a(2)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes and the horizontal one has no 2-cell column starting at level 0.

%p a:= n-> `if`(n=1, 1, (n^2-3*n+4)*(n-2)!/2): seq(a(n), n=1..23);

%Y Cf. A121634, A001710.

%K nonn,easy

%O 1,3

%A _Emeric Deutsch_, Aug 13 2006

%E Missing a(1) inserted by _Alois P. Heinz_, Nov 25 2018