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

Author

N. J. A. Sloane, Jul 12 2014

Keywords

• nonn

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.

Crossrefs

Cf. A234950.

Programs

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 *)

PARI

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

Formula

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

Extensions

More terms from Michel Marcus, Apr 06 2018