A349115 a(n) = 8^n * P(n, 3*n), where P(n, x) is n-th Legendre polynomial.

1, 24, 3424, 926208, 369378816, 194988441600, 128184980586496, 100904418485993472, 92542260511611682816, 96909547417109671182336, 114095278582299648325582848, 149184455262733048487847395328, 214496285274348399077675463868416, 336346643957900669242934177071890432

Offset: 0

Author

Vaclav Kotesovec, Nov 08 2021

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A008316, A110129, A349113, A349114.

Programs

Mathematica

Table[8^n*LegendreP[n, 3*n], {n, 0, 15}]

PARI

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

Formula

a(n) ~ 2^(4*n) * 3^n * n^(n - 1/2) / sqrt(Pi).