A349114 a(n) = 4^n * P(n, 2*n), where P(n, x) is n-th Legendre polynomial.

1, 8, 376, 33984, 4526176, 797459200, 174910868224, 45926958135296, 14047764722238976, 4905641267399503872, 1925859774286175997952, 839619968812285810868224, 402496047174560754869846016, 210424519428145503482634174464, 119148510992477432889126160826368

Offset: 0

Author

Vaclav Kotesovec, Nov 08 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A008316, A110129, A349077, A349115.

Programs

Mathematica

Table[4^n*LegendreP[n, 2*n], {n, 0, 16}]

PARI

a(n) = 4^n*pollegendre(n, 2*n); \\ Michel Marcus, Nov 08 2021

Formula

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