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

0,2

Comments

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

Links

Table of n, a(n) for n=0..13.

Eric Weisstein's World of Mathematics, Legendre Polynomial.

Wikipedia, Legendre polynomials.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A008316, A110129, A349113, A349114.

Sequence in context: A088731 A299697 A072529 * A159681 A275569 A071639

Adjacent sequences: A349112 A349113 A349114 * A349116 A349117 A349118

Keyword

nonn

Author

Vaclav Kotesovec, Nov 08 2021

Status

approved