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 A372184 #17 May 23 2024 02:40:41
%S A372184 1,9,675,198450,160744500,291751267500,1035425248357500,
%T A372184 6523179064652250000,67867154988642009000000,
%U A372184 1102501932790489436205000000,26741184379833321275152275000000,933641711437500579000666529350000000,45515033432578153226282493305812500000000
%N A372184 a(n) = 2^(1-3*n)*((2*n)!)^2/n.
%F A372184 a(n) = Product_{k=1..n-1} A339483(k).
%F A372184 a(n) = A139757(n-1)*8^(1-n)*A134372(n-1).
%F A372184 a(n) = (2^n*n*2*Zeta_k(1-2*n)*Pi^(4*n))/(D_k^(2*n-1)*sqrt(D_k)*Zeta_k(2*n)) where Zeta_k() is the Dedekind zeta function over a real quadratic field with fundamental discriminant D_k = A003658(m) for some m > 1.
%F A372184 a(n) = 8^(1-n)*Integral_{x>=0} ( x^(2*n-(1/2))*BesselK(1, 2*sqrt(x)) ), where BesselK(m, ...) is the modified Bessel function K_m(...) of the first kind.
%F A372184 Sum_{n>=1} (x^(n-1)/a(n)) = (BesselI(1, 2*2^(3/4)*x^(1/4)) - BesselJ(1, 2*2^(3/4)*x^(1/4)))/(4*2^(1/4)*x^(3/4))
%F A372184 = (d/dx)((-2 + BesselI(0, 2*2^(3/4)*x^(1/4)) + BesselJ(0, 2*2^(3/4)*x^(1/4)))/4), where BesselI(m, ...) is the modified Bessel function I_m(...) of the first kind and BesselJ(m, ...) is the Bessel function J_m(...) of the first kind.
%F A372184 a(n) ~ Pi*2^(n+3)*exp(-4*n)*n^(4*n). - _Stefano Spezia_, Apr 22 2024
%F A372184 D-finite with recurrence 2*a(n) -n*(n-1)*(-1+2*n)^2*a(n-1)=0. - _R. J. Mathar_, May 20 2024
%o A372184 (PARI) a(n) = 2^(1-3*n)*(2*n)!^2/n
%Y A372184 Cf. A370411, A370412.
%Y A372184 Cf. A003658, A139757, A134372, A339483.
%K A372184 nonn
%O A372184 1,2
%A A372184 _Thomas Scheuerle_, Apr 21 2024