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%I #9 Nov 08 2021 04:28:01
%S 1,8,376,33984,4526176,797459200,174910868224,45926958135296,
%T 14047764722238976,4905641267399503872,1925859774286175997952,
%U 839619968812285810868224,402496047174560754869846016,210424519428145503482634174464,119148510992477432889126160826368
%N a(n) = 4^n * P(n, 2*n), where P(n, x) is n-th Legendre polynomial.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LegendrePolynomial.html">Legendre Polynomial</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legendre polynomials</a>.
%F a(n) ~ 2^(4*n) * n^(n - 1/2) / sqrt(Pi).
%t Table[4^n*LegendreP[n, 2*n], {n, 0, 16}]
%o (PARI) a(n) = 4^n*pollegendre(n, 2*n); \\ _Michel Marcus_, Nov 08 2021
%Y Cf. A008316, A110129, A349077, A349115.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 08 2021
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