A292693 Sum over all Dyck paths of semilength n of products over all peaks p of (x_p+n*y_p)/y_p, where x_p and y_p are the coordinates of peak p.

1, 2, 18, 268, 5500, 143046, 4491340, 164927288, 6926613912, 327225762250, 17166979868764, 989951268341124, 62226648527948008, 4234070369464440974, 310027061374942635000, 24305529829528548674800, 2031272969339630171158576, 180267634530033586511045778

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = A258219(n,n).

a(n) ~ 2^(3/2) * 3^((3*n-1)/2) * n^(n + 1/2) / (sqrt(Pi) * exp(n)). - Vaclav Kotesovec, Jul 19 2021

Crossrefs

Main diagonal of A258219.

Sequence in context: A032037 A351276 A138275 * A351275 A364400 A334242

Adjacent sequences: A292690 A292691 A292692 * A292694 A292695 A292696

Keyword

nonn

Author

Alois P. Heinz, Sep 20 2017

Status

approved