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 A290882 #7 Aug 27 2017 19:58:49
%S A290882 1,1,1,-1,-7,25,265,-1705,-24175,227665,4037425,-50333425,-1070526775,
%T A290882 16655398825,412826556025,-7711225809625,-218150106913375,
%U A290882 4760499335502625,151297155973926625,-3779764853639958625,-133288452772763494375,3752942823715824285625,145378048431548466795625,-4556465805050372544735625,-192296944484564858674279375,6641455313355871353308640625
%N A290882 E.g.f. E(x) = C(x) + S(x) such that C(x)^2 - S(x)^2 = 1 and C'(x)^2 + S'(x)^2 = 1, where C(x) is the e.g.f. of A290880 and S(x) is the e.g.f. of A290881.
%H A290882 Paul D. Hanna, <a href="/A290882/b290882.txt">Table of n, a(n) for n = 0..100</a>
%F A290882 E.g.f.: E(x) = exp( Series_Reversion( Integral sqrt( cosh(2*x) ) dx ) ).
%e A290882 E.g.f.: E(x) = 1 + x + x^2/2! - x^3/3! - 7*x^4/4! + 25*x^5/5! + 265*x^6/6! - 1705*x^7/7! - 24175*x^8/8! + 227665*x^9/9! + 4037425*x^10/10! - 50333425*x^11/11! - 1070526775*x^12/12! + 16655398825*x^13/13! + 412826556025*x^14/14! - 7711225809625*x^15/15! - 218150106913375*x^16/16! +...
%e A290882 such that E(x) = C(x) + S(x) where
%e A290882 S(x) = x - x^3/3! + 25*x^5/5! - 1705*x^7/7! + 227665*x^9/9! - 50333425*x^11/11! + 16655398825*x^13/13! - 7711225809625*x^15/15! + 4760499335502625*x^17/17! - 3779764853639958625*x^19/19! + 3752942823715824285625*x^21/21! +...
%e A290882 C(x) = 1 + x^2/2! - 7*x^4/4! + 265*x^6/6! - 24175*x^8/8! + 4037425*x^10/10! - 1070526775*x^12/12! + 412826556025*x^14/14! - 218150106913375*x^16/16! + 151297155973926625*x^18/18! - 133288452772763494375*x^20/20! +...
%e A290882 These series satisfy: C(x)^2 - S(x)^2 = 1 and C'(x)^2 + S'(x)^2 = 1.
%o A290882 (PARI) {a(n) = my(C=1,S=x); for(i=1,n, C = 1 + intformal( S/sqrt(C^2 + S^2 + O(x^(n+2))) ); S = intformal( C/sqrt(C^2 + S^2)) ); n!*polcoeff(C + S,n)}
%o A290882 for(n=0,30, print1(a(n),", "))
%o A290882 (PARI) {a(n) = my(E=1); E = exp( serreverse( intformal( sqrt(cosh(2*x + O(x^(n+2)))) ) )); n!*polcoeff(E,n)}
%o A290882 for(n=0,30, print1(a(n),", "))
%Y A290882 Cf. A290879, A290880, A290881, A290883.
%K A290882 sign
%O A290882 0,5
%A A290882 _Paul D. Hanna_, Aug 13 2017