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 A184892 #10 Oct 07 2020 07:52:54
%S A184892 1,40,8100,2310000,768075000,278719056000,107022956040000,
%T A184892 42753018765600000,17585519046944062500,7397979398239787500000,
%U A184892 3168258657090171394750000,1376657183877933677265000000
%N A184892 a(n) = C(2n,n) * (5^n/n!^2) * Product_{k=0..n-1} (5k+1)*(5k+4).
%F A184892 Self-convolution of A184891, where
%F A184892 . A184891(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+1)*(10k+4).
%F A184892 a(n) ~ sqrt(5 - sqrt(5)) * 2^(2*n - 3/2) * 5^(3*n) / (Pi^(3/2) * n^(3/2)). - _Vaclav Kotesovec_, Oct 07 2020
%e A184892 G.f.: A(x) = 1 + 40*x + 8100*x^2 + 2310000*x^3 +...
%e A184892 A(x)^(1/2) = 1 + 20*x + 3850*x^2 + 1078000*x^3 +...+ A184891(n)*x^n +...
%t A184892 Table[Binomial[2*n, n] * 5^n / n!^2 * Product[(5*k + 1)*(5*k + 4), {k, 0, n - 1}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 07 2020 *)
%o A184892 (PARI) {a(n)=(2*n)!/n!^2*(5^n/n!^2)*prod(k=0,n-1,(5*k+1)*(5*k+4))}
%Y A184892 Cf. A184891, A184890, A184423, A008977, A001421, A184896, A184898.
%K A184892 nonn
%O A184892 0,2
%A A184892 _Paul D. Hanna_, Jan 25 2011