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A201687 a(1)=0; a(n) = b(n) - Sum_{r=1..n-1} a(r)*b(n-1-r), where b(n) = A000085(n).

%I A201687 #23 Apr 15 2022 10:32:44
%S A201687 0,2,2,6,14,44,134,462,1616,6062,23306,93996,389102,1671158,7360256,
%T A201687 33418374,155359922,741476492,3617591462,18065875422,92087408048,
%U A201687 479382896030,2543670789962,13759520646636,75769638724382,424727826838886,2420944511425472
%N A201687 a(1)=0; a(n) = b(n) - Sum_{r=1..n-1} a(r)*b(n-1-r), where b(n) = A000085(n).
%H A201687 J.-L. Baril, <a href="https://doi.org/10.37236/665">Classical sequences revisited with permutations avoiding dotted pattern</a>, Electronic Journal of Combinatorics, 18 (2011), #P178. See Table 3.
%p A201687 b:= proc(n) option remember; `if`(n<1, 1, b(n-1)+(n-1)*b(n-2)) end:
%p A201687 a:= proc(n) option remember; `if`(n<2, 0,
%p A201687       b(n)-add(a(r)*b(n-1-r), r=1..n-1))
%p A201687     end:
%p A201687 seq(a(n), n=1..28);  # _Alois P. Heinz_, Apr 14 2022
%t A201687 b[n_] := b[n] = If[n < 1, 1, b[n - 1] + (n - 1)*b[n - 2]];
%t A201687 a[n_] := a[n] = If[n < 2, 0, b[n] - Sum[a[r]*b[n - 1 - r], {r, 1, n - 1}]];
%t A201687 Table[a[n], {n, 1, 28}] (* _Jean-François Alcover_, Apr 15 2022, after _Alois P. Heinz_ *)
%Y A201687 Cf. A000085, A201689.
%K A201687 nonn
%O A201687 1,2
%A A201687 _N. J. A. Sloane_, Dec 03 2011