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 A273033 E.g.f.: (sin(3*x) + sin(4*x)) / sin(7*x). 2
 1, 12, 732, 109332, 30406812, 13587056052, 8904250650492, 8045727017033172, 9586782871360007772, 14564334832981893064692, 27477080512619965247054652, 63024425641459625896776174612, 172720667970739808701108304367132, 557383361208023769780400587942586932, 2092050338949043346342979863638489321212, 9036239176876728629700436615577988154925652 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA E.g.f.: cos(x/2) / cos(7*x/2). E.g.f.: (cos(3*x) + cos(4*x)) / (1 + cos(7*x)). E.g.f.: (exp(3*i*x) + exp(4*i*x)) / (1 + exp(7*i*x)), where i^2 = -1. E.g.f.: exp(3*i*x)/(1 + exp(7*i*x)) + exp(-3*i*x)/(1 + exp(-7*i*x)), where i^2 = -1. O.g.f.: 1/(1 - 3*4*x/(1 - 7^2*x/(1 - 10*11*x/(1 - 14^2*x/(1 - ... - (7*n+3)*(7*n+4)*x/(1 - (7*n+7)^2*x/(1 - ...))))))), a continued fraction. a(n) ~ (2*n)! * 4*cos(Pi/14) * 7^(2*n) / Pi^(2*n+1). - Vaclav Kotesovec, May 14 2016 From Peter Bala, May 13 2017: (Start) G.f.: 1/(1 + 9*x - 21*x/(1 - 28*x/(1 + 9*x - 140*x/(1 - 154*x/(1 + 9*x - ... - 7*n*(7*n-4)*x/(1 - 7*n*(7*n-3)*x/(1 + 9*x - ... G.f.: 1/(1 + 16*x - 28*x/(1 - 21*x/(1 + 16*x - 154*x/(1 - 140*x/(1 + 16*x - ... - 7*n*(7*n-3)*x/(1 - 7*n*(7*n-4)*x/(1 + 16*x - .... (End) EXAMPLE E.g.f.: A(x) = 1 + 12*x^2/2! + 732*x^4/4! + 109332*x^6/6! + 30406812*x^8/8! + 13587056052*x^10/10! + 8904250650492*x^12/12! +... such that A(x) = (sin(3*x) + sin(4*x)) / sin(7*x). O.g.f.: F(x) = 1 + 12*x + 732*x^2 + 109332*x^3 + 30406812*x^4 + 13587056052*x^5 + 8904250650492*x^6 + 8045727017033172*x^7 +... such that the o.g.f. can be expressed as the continued fraction: F(x) = 1/(1 - 3*4*x/(1 - 7^2*x/(1 - 10*11*x/(1 - 14^2*x/(1 - 17*18*x/(1 - 21^2*x/(1 - 24*25*x/(1 - 28^2*x/(1 - 31*32*x/(1 - 35^2*x/(1 - 38*39*x/(1 - ...)))))))))))). MATHEMATICA With[{nn=40}, Take[CoefficientList[Series[(Sin[3x]+Sin[4x])/Sin[7x], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Sep 23 2019 *) PROG (PARI) {a(n) = my(A=1, X=x+x*O(x^(2*n+1))); (2*n)! * polcoeff( (sin(3*X) + sin(4*X))/sin(7*X), 2*n)} for(n=0, 20, print1(a(n), ", ")) (PARI) {a(n) = my(A=1, X=x+x*O(x^(2*n+1))); (2*n)! * polcoeff( (cos(3*X) + cos(4*X))/(1 + cos(7*X)), 2*n)} for(n=0, 20, print1(a(n), ", ")) (PARI) {a(n) = my(A=1, X=x+x*O(x^(2*n+1))); (2*n)! * polcoeff( (exp(3*I*X) + exp(4*I*X))/(1 + exp(7*I*X)), 2*n)} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A272158, A272467, A273031, A273032, A156196. Sequence in context: A341560 A317337 A089036 * A276636 A284769 A201246 Adjacent sequences:  A273030 A273031 A273032 * A273034 A273035 A273036 KEYWORD nonn AUTHOR Paul D. Hanna, May 13 2016 STATUS approved

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Last modified May 22 06:54 EDT 2022. Contains 353933 sequences. (Running on oeis4.)