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

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%I A349077 #16 Feb 16 2025 08:34:02
%S A349077 1,4,886,575296,748553926,1638884021248,5430931463592636,
%T A349077 25386301852394340352,159203574262026117932614,
%U A349077 1290247693627696897075707904,13126820230906199855332092508756,163819123650250694146607819756929024,2460884002303138397686849151579559249436
%N A349077 a(n) = 4^n * P(2*n, n), where P(n, x) is n-th Legendre polynomial.
%H A349077 Vaclav Kotesovec, <a href="/A349077/b349077.txt">Table of n, a(n) for n = 0..175</a>
%H A349077 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LegendrePolynomial.html">Legendre Polynomial</a>.
%H A349077 Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legendre polynomials</a>.
%F A349077 a(n) ~ 2^(4*n - 1/2) * n^(2*n - 1/2) / sqrt(Pi).
%t A349077 Table[4^n*LegendreP[2*n, n], {n, 0, 15}]
%o A349077 (PARI) a(n) = 4^n*pollegendre(2*n, n); \\ _Michel Marcus_, Nov 08 2021
%Y A349077 Cf. A008316, A110129.
%K A349077 nonn
%O A349077 0,2
%A A349077 _Vaclav Kotesovec_, Nov 07 2021