Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Nov 08 2021 04:27:57
%S 1,8,40636,748832256,37759888297756,4086692369433395200,
%T 815254385427670754825764,270587150855247020644760551424,
%U 138859707622050969870951620062449436,104286590422721059977069662227099300134912,109828573459404650800550127862919905133973562480
%N a(n) = 8^n * P(3*n, n), where P(n, x) is n-th Legendre polynomial.
%C In general, for k>=1, P(k*n, n) ~ 2^(k*n) * n^(k*n) / sqrt(k*Pi*n).
%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^(6*n) * n^(3*n - 1/2) / sqrt(3*Pi).
%t Table[8^n*LegendreP[3*n, n], {n, 0, 12}]
%o (PARI) a(n) = 8^n*pollegendre(3*n, n); \\ _Michel Marcus_, Nov 08 2021
%Y Cf. A008316, A110129, A349077, A349115.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 08 2021