A369327 a(n) is the number of words of length n over the alphabet [n] and sortable by a (2,1)-pop stack of depth 2.

1, 1, 4, 24, 149, 923, 5784, 36708, 235156, 1516864, 9838018, 64093998, 419137378, 2749637566, 18087479624, 119263349200, 788015054253, 5216212564723, 34584497597602, 229635524379026, 1526740206967913, 10162620233598959, 67719554546286284, 451699650863065424

Offset: 0

Author

Stefano Spezia, Jan 20 2024

Keywords

• nonn

Links

• Toufik Mansour, Howard Skogman, and Rebecca Smith, Sorting inversion sequences, arXiv:2401.06662 [math.CO], 2024. See Theorem 3.25 at page 13.

Crossrefs

Main diagonal of A369326.

Cf. A369325.

Programs

Mathematica

A369326[n_,k_]:=SeriesCoefficient[((1-x)(1-2x)-((1-x)(1-2x)+x^2)y)/((1-x)(1-2x)-(1-x)(2-3x)y+(1-2x)y^2),{x,0,n},{y,0,k}]; a[n_]:=A369326[n,n]; Array[a,24,0]

Formula

a(n) = A369326(n, n).