A093346 Array read by antidiagonals: T(r,n) = number of two-stack sortable r-permutations.

1, 1, 2, 1, 3, 6, 1, 4, 15, 22, 1, 5, 28, 95, 91, 1, 6, 45, 252, 690, 408, 1, 7, 66, 525, 2618, 5481, 1938, 1, 8, 91, 946, 7095, 29848, 46376, 9614, 1, 9, 120, 1547, 15741, 105417, 363216, 411255, 49335, 1, 10, 153, 2360, 30576, 288288, 1673535, 4638348, 3781635, 260130

Offset

1,3

Links

Table of n, a(n) for n=1..55.

D. Xu, Generalizations of two-stack-sortable permutations, PhD thesis, arXiv:math/0209313 [math.CO], 2002.

Formula

T(r,n) = 2(r+1) * ((2r+1)n)!/[n!*(2rn+2)! ].

Mathematica

T[r_, n_] := 2(r+1) * ((2r+1)n)!/(n!*(2r n+2)!); Table[T[r-n+1, n], {r, 1, 10}, {n, 1, r}] // Flatten (* Jean-François Alcover, Feb 18 2019 *)

Prog

(PARI) T(r, n)=2*(r+1)*((2*r+1)*n)!/(n!*(2*r*n+2)!)

Crossrefs

Cf. A000139.

Sequence in context: A360858 A181511 A115196 * A115597 A325007 A103371

Adjacent sequences: A093343 A093344 A093345 * A093347 A093348 A093349

Keyword

nonn,tabl

Author

Ralf Stephan, Apr 26 2004

Status

approved