A349077 a(n) = 4^n * P(2*n, n), where P(n, x) is n-th Legendre polynomial.

1, 4, 886, 575296, 748553926, 1638884021248, 5430931463592636, 25386301852394340352, 159203574262026117932614, 1290247693627696897075707904, 13126820230906199855332092508756, 163819123650250694146607819756929024, 2460884002303138397686849151579559249436

Offset: 0

Author

Vaclav Kotesovec, Nov 07 2021

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..175
• Eric Weisstein's World of Mathematics, Legendre Polynomial.
• Wikipedia, Legendre polynomials.

Crossrefs

Cf. A008316, A110129.

Programs

Mathematica

Table[4^n*LegendreP[2*n, n], {n, 0, 15}]

PARI

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

Formula

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