This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A364520 #19 Oct 05 2023 08:37:22
%S A364520 1,64,12012,2621440,608435100,146028888064,35794148650260,
%T A364520 8901646138474496,2237242000722428700,566823049100850626560,
%U A364520 144520856111821003326512,37036782455383679028953088,9531607276865293630675462980,2461693334077582876433071472640
%N A364520 a(n) = (7*n)!*(n/2)!/((7*n/2)!*(n)!*(3*n)!).
%C A364520 Row 4 of A364519.
%H A364520 Paolo Xausa, <a href="/A364520/b364520.txt">Table of n, a(n) for n = 0..400</a>
%F A364520 a(n) = [x^(3*n)] ( (1 + x)^7/(1 - x) )^n.
%F A364520 a(n) = Sum_{j = 0..3*n} binomial(7*n, j)*binomial(4*n-j-1, 3*n-j).
%F A364520 a(n) = binomial(4*n-1, 3*n) * hypergeom([-7*n, -3*n], [1 - 4*n], -1) for n >= 2.
%F A364520 a(n) ~ c^n * 1/sqrt(6*Pi*n) where c = (14/3)^3*sqrt(7).
%F A364520 P-recursive: a(n) = 448*(7*n-1)*(7*n-3)*(7*n-5)*(7*n-9)*(7*n-11)*(7*n-13)/(3*n*(3*n-1)*(3*n-2)*(3*n-3)*(3*n-4)*(3*n-5)) * a(n-2) with a(0) = 1 and a(1) = 64.
%F A364520 The generating function is an algebraic function over the field of rational functions Q(x).
%p A364520 seq( simplify((7*n)!*(n/2)!/((7*n/2)!*(n)!*(3*n)!)), n = 0..15);
%t A364520 A364520[n_]:=(7n)!(n/2)!/((7n/2)!n!(3n)!);Array[A364520,15,0] (* _Paolo Xausa_, Oct 05 2023 *)
%o A364520 (Python)
%o A364520 from math import factorial
%o A364520 from sympy import factorial2
%o A364520 def A364520(n): return int((factorial(7*n)*factorial2(n)<<(3*n))//(factorial2(7*n)*factorial(n)*factorial(3*n))) # _Chai Wah Wu_, Aug 13 2023
%Y A364520 Cf. A276098, A364519.
%K A364520 nonn,easy
%O A364520 0,2
%A A364520 _Peter Bala_, Aug 09 2023