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A244887 Third column of triangle in A234950. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A203605 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

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Last modified February 21 11:36 EST 2019. Contains 320372 sequences. (Running on oeis4.)