A264460 Number of permutations of [n] with exactly one occurrence of the generalized pattern 23-1.

1, 6, 32, 171, 944, 5444, 32919, 208816, 1388240, 9657929, 70187054, 531857288, 4194927585, 34379859346, 292303350268, 2574284790795, 23450837821836, 220681535036288, 2142618638738279, 21438586249394500, 220827871704427308, 2339281577294955745

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..500

Example

a(3) = 1: 231.
a(4) = 6: 1342, 2314, 2413, 2431, 3241, 4231.

Maple

b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
      b(u-j, o+j-1), j=1..u) +add(convert(series(
      b(u+j-1, o-j)*x^u, x, 2), polynom), j=1..o))
    end:
a:= n-> coeff(b(n, 0), x, 1):
seq(a(n), n=3..25);

Mathematica

b[u_, o_] := b[u, o] = If[u+o == 0, 1, Sum[b[u-j, o+j-1], {j, 1, u}] + Sum[Series[b[u+j-1, o-j] x^u, {x, 0, 2}] // Normal, {j, 1, o}]];
a[n_] := Coefficient[b[n, 0], x, 1];
a /@ Range[3, 25] (* Jean-François Alcover, Sep 28 2020, after Maple *)

Crossrefs

Column k=1 of A260670.

Sequence in context: A306900 A137637 A125190 * A180037 A277742 A000558

Adjacent sequences: A264457 A264458 A264459 * A264461 A264462 A264463

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2015

Status

approved