cp's OEIS Frontend

A215638 E.g.f.: Series_Reversion( x/(cos(x) + sin(x)) ).

%I A215638 #10 Jan 22 2014 16:43:08
%S A215638 1,2,3,-16,-255,-1824,875,279040,5019777,34163200,-822579021,
%T A215638 -35005820928,-598199789759,1612679634944,456446015789595,
%U A215638 15087057004396544,168732823928006145,-8490541860738957312,-560665092239473776157,-14661549133472721797120
%N A215638 E.g.f.: Series_Reversion( x/(cos(x) + sin(x)) ).
%C A215638 Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.991787... - _Vaclav Kotesovec_, Jan 22 2014
%H A215638 Vaclav Kotesovec, <a href="/A215638/b215638.txt">Table of n, a(n) for n = 1..400</a>
%F A215638 E.g.f. satisfies: A(x) = x * (cos(A(x)) + sin(A(x))).
%F A215638 a(n) = [x^n/n!] x*(cos(x)+sin(x))^n / n.
%F A215638 a(n) = n*A215639(n-1).
%e A215638 E.g.f.: A(x) = x + 2*x^2/2! + 3*x^3/3! - 16*x^4/4! - 255*x^5/5! - 1824*x^6/6! +...
%e A215638 where A(x/(cos(x) + sin(x))) = x and A(x) = x*(cos(A(x)) + sin(A(x))).
%e A215638 Related expansions:
%e A215638 cos(A(x)) = 1 - x^2/2! - 6*x^3/3! - 23*x^4/4! + 40*x^5/5! + 2159*x^6/6! + 26656*x^7/7! + 114577*x^8/8! +...
%e A215638 sin(A(x)) = x + 2*x^2/2! + 2*x^3/3! - 28*x^4/4! - 344*x^5/5! - 2034*x^6/6! + 8224*x^7/7! + 443176*x^8/8! +...
%t A215638 Rest[CoefficientList[InverseSeries[Series[x/(Sqrt[2]*Cos[Pi/4-x]),{x,0,20}],x],x]*Range[0,20]!] (* _Vaclav Kotesovec_, Jan 22 2014 *)
%o A215638 (PARI) {a(n)=local(X=x+x^2*O(x^n)); n!*polcoeff(serreverse(x/(cos(X)+sin(X))), n)}
%o A215638 (PARI) {a(n)=local(X=x+x^2*O(x^n)); n!*polcoeff(x*(cos(X)+sin(X))^n/n, n)}
%o A215638 (PARI) {a(n)=local(A=x+x^2*O(x^n)); for(i=1,n,A=x*(cos(A)+sin(A)));n!*polcoeff(A, n)}
%o A215638 for(n=1, 31, print1(a(n), ", "))
%Y A215638 Cf. A215368, A215639.
%K A215638 sign
%O A215638 1,2
%A A215638 _Paul D. Hanna_, Aug 18 2012