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 A227051 E.g.f.: 1/(cos(x) - sin(x)*sinh(x)), omitting the zero-valued coefficients of odd powers of x. 0

%I

%S 1,3,53,2333,191673,25307913,4900979093,1308599657693,460755584003313,

%T 206844794964734673,115313659955341400333,78158334287649490486853,

%U 63294640267864707577746153,60357724113527363258814802233,66943314938342593826952764256773,85443499990582824984241143043808813

%N E.g.f.: 1/(cos(x) - sin(x)*sinh(x)), omitting the zero-valued coefficients of odd powers of x.

%F a(n) == 3 (mod 10) for n>0 (conjecture).

%F a(n) ~ 2*(2*n)! / ((sin(r)+cos(r)*sinh(r)+sin(r)*cosh(r)) * r^(2*n+1)), where r = 0.825607669071161851569946... is the root of the equation sin(r)*sinh(r) = cos(r). - _Vaclav Kotesovec_, Jul 13 2014

%e E.g.f.: A(x) = 1 + 3*x^2/2! + 53*x^4/4! + 2333*x^6/6! + 191673*x^8/8! + 25307913*x^10/10! +...

%t Table[n!*SeriesCoefficient[1/(Cos[x] - Sin[x]*Sinh[x]),{x,0,n}],{n,0,40,2}] (* _Vaclav Kotesovec_, Jul 13 2014 *)

%o (PARI) {a(n)=local(X=x+x*O(x^(2*n))); (2*n)!*polcoeff(1/(cos(X) - sin(X)*sinh(X)), 2*n)}

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

%Y Cf. A185071.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 29 2013

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Last modified January 25 15:34 EST 2022. Contains 350572 sequences. (Running on oeis4.)