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 A272467 E.g.f.: (sin(2*x) + sin(3*x)) / sin(5*x). 7
 1, 6, 186, 14166, 2009946, 458225526, 153212718906, 70632832168086, 42939614599671066, 33282798350926545846, 32036398991671262130426, 37490905748197466281582806, 52420996658289450763331680986, 86309558223400912513674314622966, 165280246718130394753827229389826746, 364233987506387128128991081880073730326, 915234544675507984101674168382043517591706 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..200 P. Bala, Some S-fractions related to the expansions of sin(ax)/cos(bx) and cos(ax)/cos(bx) FORMULA E.g.f.: cos(x/2) / cos(5*x/2). E.g.f.: (cos(2*x) + cos(3*x)) / (1 + cos(5*x)). E.g.f.: (exp(2*i*x) + exp(3*i*x)) / (1 + exp(5*i*x)), where i^2 = -1. E.g.f.: exp(2*i*x)/(1 + exp(5*i*x)) + exp(-2*i*x)/(1 + exp(-5*i*x)), where i^2 = -1. O.g.f.: 1/(1 - 2*3*x/(1 - 5^2*x/(1 - 7*8*x/(1 - 10^2*x/(1 - ... - (5*n+2)*(5*n+3)*x/(1 - (5*n+5)^2*x/(1 - ...))))))), a continued fraction. a(n) = 6 (mod 10) for n>0. a(n) ~ (2*n)! * sqrt(2*(5 + sqrt(5))) * 5^(2*n) / Pi^(2*n+1). - Vaclav Kotesovec, Apr 30 2016 From Peter Bala, May 13 2017: (Start) G.f.: 1/(1 + 4*x - 10*x/(1 - 15*x/(1 + 4*x - 70*x/(1 - 80*x/(1 + 4*x - ... - 5*n*(5*n-3)*x/(1 - 5*n*(5*n-2)*x/(1 + 4*x - .... G.f.: 1/(1 + 9*x - 15*x/(1 - 10*x/(1 + 9*x - 80*x/(1 - 70*x/(1 + 9*x - ... - 5*n*(5*n-2)*x/(1 - 5*n*(5*n-3)*x/(1 + 9*x - .... (End) EXAMPLE E.g.f.: A(x) = 1 + 6*x^2/2! + 186*x^4/! + 14166*x^6/6! + 2009946*x^8/8! + 458225526*x^10/10! + 153212718906*x^12/12! +... such that A(x) = (sin(2*x) + sin(3*x)) / sin(5*x). O.g.f.: F(x) = 1 + 6*x + 186*x^2 + 14166*x^3 + 2009946*x^4 + 458225526*x^5 + 153212718906*x^6 + 70632832168086*x^7 + 42939614599671066*x^8 +... such that the o.g.f. can be expressed as the continued fraction: F(x) = 1/(1 - 2*3*x/(1 - 5^2*x/(1 - 7*8*x/(1 - 10^2*x/(1 - 12*13*x/(1 - 15^2*x/(1 - 17*18*x/(1 - 20^2*x/(1 - 22*23*x/(1 - 25^2*x/(1 - 27*28*x/(1 - ...)))))))))))). MATHEMATICA With[{nn=40}, Take[CoefficientList[Series[(Sin[2x]+Sin[3x])/Sin[5x], {x, 0, nn}], x] Range[ 0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Jun 12 2022 *) PROG (PARI) {a(n) = my(A=1, X=x+x*O(x^(2*n+1))); (2*n)! * polcoeff( (sin(2*X) + sin(3*X))/sin(5*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(2*X) + cos(3*X))/(1 + cos(5*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(2*I*X) + exp(3*I*X))/(1 + exp(5*I*X)), 2*n)} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A272158, A272468, A156185. Sequence in context: A175237 A222335 A037298 * A015004 A324094 A129046 Adjacent sequences: A272464 A272465 A272466 * A272468 A272469 A272470 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 30 2016 STATUS approved

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Last modified December 1 06:44 EST 2023. Contains 367468 sequences. (Running on oeis4.)