A244887 Third column of triangle in A234950.

2, 20, 135, 770, 4004, 19656, 92820, 426360, 1918620, 8498776, 37182145, 161056350, 691945800, 2952675600, 12527780760, 52895074320, 222399744300, 931689977400, 3890668331550, 16201562020644, 67298796085752, 278927990831600, 1153747598439800, 4763749454427600, 19637233862140440

Offset

2,1

Comments

Remmel (2014) asks for a formula.

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..500

Jeffrey B. Remmel, Consecutive Up-down Patterns in Up-down Permutations, Electron. J. Combin., 21 (2014), #P3.2.

Formula

a(n) = A234950(n, 2).

Mathematica

Table[Sum[Binomial[s, 2] Binomial[n+s, n] (n - s + 1) / (n + 1), {s, 2, n}], {n, 2, 15}] (* Vincenzo Librandi, Apr 06 2018 *)

Prog

(PARI) a(n) = sum(s=2, n, binomial(s, 2)*binomial(n+s, n)*(n-s+1)/(n+1)); \\ Michel Marcus, Apr 06 2018

Crossrefs

Cf. A234950.

Sequence in context: A373614 A094254 A093647 * A279112 A229454 A003490

Adjacent sequences: A244884 A244885 A244886 * A244888 A244889 A244890

Keyword

nonn

Author

N. J. A. Sloane, Jul 12 2014

Extensions

More terms from Michel Marcus, Apr 06 2018

Status

approved