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 A273378 #11 Nov 24 2023 12:12:36
%S A273378 1,1,3,31,553,18961,874203,62142991,5423159953,655008561121,
%T A273378 92608009666803,16986382591132351,3541042896979933753,
%U A273378 917218574919912685681,264626392137250618729803,91981994791776047627320111,35093294931542583405745553953,15761280495157673681620641704641,7683715734173928801016321555135203,4330739041520082271329522758307378271,2626405828066727295503315986000018932553
%N A273378 Expansion of sqrt( cosh(x) / cos(x) ) = Sum_{n>=0} a(n) * x^(2n) / (2n)!.
%C A273378 All terms seem to be odd.
%e A273378 E.g.f.: A(x) = 1 + x^2/2! + 3*x^4/4! + 31*x^6/6! + 553*x^8/8! + 18961*x^10/10! + 874203*x^12/12! + 62142991*x^14/14! + 5423159953*x^16/16! + 655008561121*x^18/18! +...
%e A273378 where A(x)^2 = cosh(x) / cos(x):
%e A273378 A(x)^2 = 1 + 2*x^2 + 12*x^4 + 152*x^6 + 3472*x^8 + 126752*x^10 + 6781632*x^12 + 500231552*x^14 +...+ A000795(n)*x^(2*n)/(2*n)! +...
%o A273378 (PARI) {a(n) = (2*n)! * polcoeff( sqrt( cosh(x + x*O(x^(2*n))) / cos(x + x*O(x^(2*n))) ) , 2*n)}
%o A273378 for(n=0,20,print1(a(n),", "))
%Y A273378 Cf. A000795.
%K A273378 nonn
%O A273378 0,3
%A A273378 _Paul D. Hanna_, May 21 2016