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 A215368 #12 Oct 04 2020 11:21:12
%S A215368 1,2,15,176,2905,61536,1592703,48706048,1718376561,68702272000,
%T A215368 3069734553743,151592011714560,8198710703202825,481965222651551744,
%U A215368 30598546651134134655,2086474763912627879936,152083996930329322871521,11800530001358902191587328,971113004536128839898536079
%N A215368 E.g.f.: Series_Reversion( x*cos(x) - x*sin(x) ).
%H A215368 Vaclav Kotesovec, <a href="/A215368/b215368.txt">Table of n, a(n) for n = 1..300</a>
%F A215368 E.g.f. satisfies: A(x) = x / (cos(A(x)) - sin(A(x))).
%F A215368 a(n) = [x^n/n!] 1/(cos(x)-sin(x))^n / n.
%F A215368 a(n) = n*A201923(n-1).
%F A215368 a(n) ~ sqrt(-1 + 4/(3 + sin(2*s))) * n^(n-1) / (r^n * exp(n)), where s = 0.4026281741881116098199325239112307245635064777960... is the root of the equation s*cos(2*s) + sin(2*s) = 1 and r = s*(cos(s) - sin(s)) = 0.21266685344074710045360679397024815598865409988038310855608986167... - _Vaclav Kotesovec_, Oct 04 2020
%e A215368 E.g.f.: A(x) = x + 2*x^2/2! + 15*x^3/3! + 176*x^4/4! + 2905*x^5/5! +...
%e A215368 where A(x*cos(x) - x*sin(x)) = x and A(x) = x/(cos(A(x)) - sin(A(x))).
%e A215368 Related expansions:
%e A215368 cos(A(x)) = 1 - x^2/2! - 6*x^3/3! - 71*x^4/4! - 1160*x^5/5! - 24481*x^6/6! - 631904*x^7/7! - 19288079*x^8/8! -...
%e A215368 sin(A(x)) = x + 2*x^2/2! + 14*x^3/3! + 164*x^4/4! + 2696*x^5/5! + 57006*x^6/6! + 1473632*x^7/7! + 45026344*x^8/8! +...
%o A215368 (PARI) {a(n)=local(X=x+x^2*O(x^n));n!*polcoeff(serreverse(x*cos(X)-x*sin(X)),n)}
%o A215368 (PARI) {a(n)=local(X=x+x^2*O(x^n));n!*polcoeff(x/(cos(X)-sin(X))^n/n,n)}
%o A215368 for(n=1,31,print1(a(n),", "))
%Y A215368 Cf. A201923, A215638.
%K A215368 nonn
%O A215368 1,2
%A A215368 _Paul D. Hanna_, Aug 08 2012