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

0, 2, 2, 6, 14, 44, 134, 462, 1616, 6062, 23306, 93996, 389102, 1671158, 7360256, 33418374, 155359922, 741476492, 3617591462, 18065875422, 92087408048, 479382896030, 2543670789962, 13759520646636, 75769638724382, 424727826838886, 2420944511425472

Offset: 1

Author

N. J. A. Sloane, Dec 03 2011

Keywords

• nonn

Links

• J.-L. Baril, Classical sequences revisited with permutations avoiding dotted pattern, Electronic Journal of Combinatorics, 18 (2011), #P178. See Table 3.

Crossrefs

Cf. A000085, A201689.

Programs

Maple

b:= proc(n) option remember; `if`(n<1, 1, b(n-1)+(n-1)*b(n-2)) end:
a:= proc(n) option remember; `if`(n<2, 0,
      b(n)-add(a(r)*b(n-1-r), r=1..n-1))
    end:
seq(a(n), n=1..28);  # Alois P. Heinz, Apr 14 2022

Mathematica

b[n_] := b[n] = If[n < 1, 1, b[n - 1] + (n - 1)*b[n - 2]];
a[n_] := a[n] = If[n < 2, 0, b[n] - Sum[a[r]*b[n - 1 - r], {r, 1, n - 1}]];
Table[a[n], {n, 1, 28}] (* Jean-François Alcover, Apr 15 2022, after Alois P. Heinz *)