A273032 - OEIS

%I #15 Jul 20 2018 10:43:55

%S 1,10,590,87730,24386030,10896056050,7140660673070,6452172716731570,

%T 7688003030273049710,11679689713099591922290,

%U 22034907735675944799243950,50541665200040978421599836210,138511221399376147951707017623790,446986750662532432703671725548281330,1677694112006573410256120810193681597230,7246501185695514998554969680297128881865650

%N E.g.f.: (sin(2*x) + sin(5*x)) / sin(7*x).

%F E.g.f.: cos(3*x/2) / cos(7*x/2).

%F E.g.f.: (cos(2*x) + cos(5*x)) / (1 + cos(7*x)).

%F E.g.f.: (exp(2*i*x) + exp(5*i*x)) / (1 + exp(7*i*x)), where i^2 = -1.

%F E.g.f.: exp(2*i*x)/(1 + exp(7*i*x)) + exp(-2*i*x)/(1 + exp(-7*i*x)), where i^2 = -1.

%F O.g.f.: 1/(1 - 2*5*x/(1 - 7^2*x/(1 - 9*12*x/(1 - 14^2*x/(1 - ... - (7*n+2)*(7*n+5)*x/(1 - (7*n+7)^2*x/(1 - ...))))))), a continued fraction.

%F a(n) ~ (2*n)! * 4*cos(3*Pi/14) * 7^(2*n) / Pi^(2*n+1). - _Vaclav Kotesovec_, May 14 2016

%e E.g.f.: A(x) = 1 + 10*x^2/2! + 590*x^4/4! + 87730*x^6/6! + 24386030*x^8/8! + 10896056050*x^10/10! + 7140660673070*x^12/12! +...

%e such that A(x) = (sin(2*x) + sin(5*x)) / sin(7*x).

%e O.g.f.: F(x) = 1 + 10*x + 590*x^2 + 87730*x^3 + 24386030*x^4 + 10896056050*x^5 + 7140660673070*x^6 + 6452172716731570*x^7 +...

%e such that the o.g.f. can be expressed as the continued fraction:

%e F(x) = 1/(1 - 2*5*x/(1 - 7^2*x/(1 - 9*12*x/(1 - 14^2*x/(1 - 16*19*x/(1 - 21^2*x/(1 - 23*26*x/(1 - 28^2*x/(1 - 30*33*x/(1 - 35^2*x/(1 - 37*40*x/(1 - ...)))))))))))).

%t With[{nn=30},Take[CoefficientList[Series[(Sin[2x]+Sin[5x])/Sin[7x],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Jul 20 2018 *)

%o (PARI) {a(n) = my(A=1, X=x+x*O(x^(2*n+1))); (2*n)! * polcoeff( (sin(2*X) + sin(5*X))/sin(7*X), 2*n)}

%o for(n=0, 20, print1(a(n), ", "))

%o (PARI) {a(n) = my(A=1, X=x+x*O(x^(2*n+1))); (2*n)! * polcoeff( (cos(2*X) + cos(5*X))/(1 + cos(7*X)), 2*n)}

%o for(n=0, 20, print1(a(n), ", "))

%o (PARI) {a(n) = my(A=1, X=x+x*O(x^(2*n+1))); (2*n)! * polcoeff( (exp(2*I*X) + exp(5*I*X))/(1 + exp(7*I*X)), 2*n)}

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A272158, A272467, A273031, A273033, A156193.

%K nonn

%O 0,2

%A _Paul D. Hanna_, May 13 2016