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 A193444 #11 Jan 27 2020 16:03:29
%S A193444 1,1,5,51,857,21045,702597,30379839,1642718865,108171928521,
%T A193444 8495805003525,782625366185355,83400601634195049,10163125433194019325,
%U A193444 1402348965454767334725,217258436356989650347095,37513434482581646048138145,7172552434209226974773867025
%N A193444 E.g.f.: exp( Sum_{n>=1} n!*x^(2*n)/(2*n)! ) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!.
%F A193444 a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n-1,2*k-1) * k! * a(n-k). - _Ilya Gutkovskiy_, Jan 27 2020
%e A193444 E.g.f.: A(x) = 1 + x^2/2! + 5*x^4/4! + 51*x^6/6! + 857*x^8/8! + 21045*x^10/10! + 702597*x^12/12! +...+ a(n)*x^n/(2*n)! +...
%e A193444 where
%e A193444 log(A(x)) = x^2/2! + 2!*x^4/4! + 3!*x^6/6! + 4!*x^8/8! + 5!*x^10/10! +...
%o A193444 (PARI) {a(n)=(2*n)!*polcoeff(exp(sum(m=1, n, m!*x^(2*m)/(2*m)!)+O(x^(2*n+1))), 2*n)}
%Y A193444 Cf. A193441, A193442, A193443, A001813 ((2*n)!/n!).
%K A193444 nonn
%O A193444 0,3
%A A193444 _Paul D. Hanna_, Jul 25 2011