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 A205572 E.g.f.: 1/(cos(x) - sinh(x)). 1
 1, 1, 3, 13, 73, 521, 4443, 44213, 502993, 6436561, 91520883, 1431459613, 24424457113, 451474855001, 8987248462923, 191682800678213, 4360821252342433, 105410131831623841, 2697863748098734563, 72885101748061044013, 2072687894252786558953 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Radius of convergence of e.g.f. is |x| < r where r = 0.703290658863965... satisfies cos(r) = sinh(r). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(2^n + k) == a(k) (mod 2^n) for k>=0, n>=1 (conjecture). E.g.f.: E(x) = 1/(cos(x) - sinh(x)) = 1/G(0) where G(k)= 1 -x/(4*k +1 - x*(4*k +1)/(4*k + 2 + x - 2*x*(2*k+1)/(4*k + 3 + x- x*(4*k+3)/(x -4*(k+1)/G(k+1))))); Radius of convergence of e.g.f.E(x)=1/G(0) is infinity; (continued fraction, 3rd kind, 5-step). - Sergei N. Gladkovskii, Jun 08 2012, Oct 03 2012 a(n) ~ n! * 2*exp(r)/((2*sin(r)*exp(r)+exp(2*r)+1)*r^(n+1)), where r = 0.7032906588639654... is defined in the comment. - Vaclav Kotesovec, Sep 22 2013 EXAMPLE E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 73*x^4/4! + 521*x^5/5! +... MATHEMATICA CoefficientList[Series[1/(Cos[x]-Sinh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 22 2013 *) PROG (PARI) {a(n)=n!*polcoeff(1/(cos(x+x*O(x^n)) - sinh(x+x*O(x^n))), n)} CROSSREFS Sequence in context: A318617 A059294 A124468 * A128196 A162161 A119013 Adjacent sequences:  A205569 A205570 A205571 * A205573 A205574 A205575 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 29 2012 STATUS approved

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Last modified June 20 18:48 EDT 2021. Contains 345199 sequences. (Running on oeis4.)