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

Author

Alois P. Heinz, Sep 20 2017

Keywords

• nonn

Links

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

Crossrefs

Main diagonal of A258219.

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