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%I #12 Sep 28 2023 12:55:45
%S 1,4,60,3328,678912,508035072,1392439459840,13965623033856000,
%T 512247880383410995200,68683284942451522425323520,
%U 33654191472236763924706696888320,60248257274480672292932706180054122496,393994689318303735728047162574735199856230400
%N a(n) = 2^(n*(n-1)/2)*Product_{j=0..n-1} (4*j+2)!/(n+2*j+1)!.
%H Michael De Vlieger, <a href="/A341275/b341275.txt">Table of n, a(n) for n = 1..60</a>
%H Philippe Di Francesco, <a href="https://arxiv.org/abs/2102.02920">Twenty Vertex model and domino tilings of the Aztec triangle</a>, arXiv:2102.02920 [math.CO], 2021.
%H Frederick Huang, <a href="https://escholarship.org/uc/item/7p96n76z">The 20 Vertex Model and Related Domino Tilings</a>, Ph. D. Dissertation, UC Berkeley, 2023. See p. 1.
%F a(n) ~ exp(1/48) * Pi^(1/4) * 2^(9*n^2/2 + n/2 + 1/3) / (sqrt(Gamma(1/4)) * A^(1/4) * n^(7/48) * 3^(9*n^2/4 + 3*n/4 - 1/24)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Feb 08 2021
%t Table[2^(n*(n-1)/2) * Product[(4*j + 2)!/(n + 2*j + 1)!, {j, 0, n-1}], {n, 1, 15}] (* _Vaclav Kotesovec_, Feb 08 2021 *)
%o (PARI) a(n) = 2^(n*(n-1)/2)*prod(j=0, n-1, (4*j+2)!/(n+2*j+1)!);
%K nonn
%O 1,2
%A _Michel Marcus_, Feb 08 2021
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