A382404 a(n) = -Sum_{k=0..n} (-1)^k * A039599(n,k)^3.

-1, 0, 18, 480, 11550, 275184, 6597360, 159629184, 3897563670, 95946708000, 2378998624860, 59359563244800, 1489281975509328, 37545821365718400, 950601539891016000, 24159023128878865920, 616066120184552310150, 15757649689979967739200

Offset: 0

Author

Seiichi Manyama, Mar 24 2025

Keywords

• sign

Links

• Pedro J. Miana, Hideyuki Ohtsuka, and Natalia Romero, Sums of powers of Catalan triangle numbers, arXiv:1602.04347 [math.NT], 2016.

Crossrefs

Cf. A039599.

Programs

PARI

a(n) = (n-1)/(2*n+1)*binomial(2*n, n)*binomial(3*n, n);

Formula

a(n) = ((n-1)/(2*n+1)) * binomial(2*n,n) * binomial(3*n,n).