A349113 a(n) = 8^n * P(3*n, n), where P(n, x) is n-th Legendre polynomial.

1, 8, 40636, 748832256, 37759888297756, 4086692369433395200, 815254385427670754825764, 270587150855247020644760551424, 138859707622050969870951620062449436, 104286590422721059977069662227099300134912, 109828573459404650800550127862919905133973562480

Offset: 0

Author

Vaclav Kotesovec, Nov 08 2021

Keywords

• nonn

Comments

In general, for k>=1, P(k*n, n) ~ 2^(k*n) * n^(k*n) / sqrt(k*Pi*n).

Links

• Eric Weisstein's World of Mathematics, Legendre Polynomial.
• Wikipedia, Legendre polynomials.

Crossrefs

Cf. A008316, A110129, A349077, A349115.

Programs

Mathematica

Table[8^n*LegendreP[3*n, n], {n, 0, 12}]

PARI

a(n) = 8^n*pollegendre(3*n, n); \\ Michel Marcus, Nov 08 2021

Formula

a(n) ~ 2^(6*n) * n^(3*n - 1/2) / sqrt(3*Pi).