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%I #12 Feb 17 2024 14:30:50
%S 1,72,5112,358976,24984600,1726182336,118527759552,8095995597312,
%T 550493745978456,37283830177899200,2516416350265032768,
%U 169320882931135520256,11361845611339758248896,760535818250019673548288,50795721177620909117683200,3385797370455910806595080192
%N a(n) = 64^n * hypergeom([-1/2, -1/2, -1/2, -n], [1, 1, 1], 1).
%F From _Vaclav Kotesovec_, Feb 17 2024: (Start)
%F Recurrence: n^3*a(n) = 8*(24*n^3 - 12*n^2 - 22*n + 19)*a(n-1) - 3072*(n-1)*(4*n^2 - 7)*a(n-2) + 131072*(n-2)*(n-1)*(2*n + 3)*a(n-3).
%F a(n) ~ 64^n * log(n)^2 * sqrt(n) / Pi^(5/2) * (1 + c1/log(n) + c2/log(n)^2), where c1 = -3.755213781237809328111261876504370048707679178356... and c2 = 14.59060543515491211393377346917067214120336575838... (End)
%p a := n -> 64^n*hypergeom([-1/2, -1/2, -1/2, -n], [1, 1, 1], 1):
%p seq(simplify(a(n)), n = 0..15);
%t a[n_] := 64^n * HypergeometricPFQ[{-1/2, -1/2, -1/2, -n}, {1, 1, 1}, 1]; Array[a, 16, 0] (* _Amiram Eldar_, Nov 12 2022 *)
%Y Cf. A358115, A358116.
%K nonn
%O 0,2
%A _Peter Luschny_, Nov 12 2022
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