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A121633 Sum of the bottom levels of the last column over 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.

%I A121633 #13 Jul 26 2022 15:19:41
%S A121633 0,0,1,9,68,527,4408,40303,403046,4393339,51955528,663383135,
%T A121633 9102982354,133668773755,2092209897524,34783032728383,612234346270510,
%U A121633 11375905660965179,222544581264066400,4572536725690159999,98456173247669999978,2217126753620449439515
%N A121633 Sum of the bottom levels of the last column over 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 A121633 a(n) = Sum(k*A121632(n,k), k>=0).
%D A121633 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%H A121633 Alois P. Heinz, <a href="/A121633/b121633.txt">Table of n, a(n) for n = 1..449</a>
%F A121633 a(1)=0; a(n) = n*a(n-1)+(n-1)!-1 for n>=2.
%F A121633 a(n)= A000254(n)- A002672(n) a(n)= n!*sum(1/k,k=1..10)- floor(n!(e-1)) [From _Gary Detlefs_, Jul 18 2010]
%F A121633 D-finite with recurrence a(n) +(-2*n-1)*a(n-1) +(n^2+2*n-4)*a(n-2) +(-2*n^2+6*n-3)*a(n-3) +(n-3)^2*a(n-4)=0. - _R. J. Mathar_, Jul 26 2022
%e A121633 a(2)=0 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, all of whose columns start at level 0.
%p A121633 a[1]:=0: for n from 2 to 23 do a[n]:=n*a[n-1]+(n-1)!-1 od: seq(a[n],n=1..23);
%t A121633 RecurrenceTable[{a[1]==0,a[n]==n*a[n-1]+(n-1)!-1},a,{n,20}] (* _Harvey P. Dale_, Dec 01 2013 *)
%Y A121633 Cf. A121632, A000254.
%K A121633 nonn
%O A121633 1,4
%A A121633 _Emeric Deutsch_, Aug 12 2006