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A318142 a(n) = denominator(n!*[z^n]((cosh(x*z) + cos(x*z))*z/(1 - exp(-z)))(1)). 1

%I

%S 1,1,3,1,15,1,21,1,15,1,33,1,1365,1,3,1,255,1,399,1,1155,1,69,1,1365,

%T 1,21,1,435,1,7161,1,19635,1,21,1,959595,1,21,1,47355,1,9933,1,2415,1,

%U 987,1,23205,1,33,1,8745,1,4389,1,8265,1,177,1,28393365,1,33

%N a(n) = denominator(n!*[z^n]((cosh(x*z) + cos(x*z))*z/(1 - exp(-z)))(1)).

%F a(2*n + 1) = 1 for n >= 0.

%F 3 divides a(2*n) for n >= 1.

%p gf := (cosh(x*z)+cos(x*z))*z/(1-exp(-z)): ser := series(gf, z, 70):

%p seq(denom(subs(x=1, n!*coeff(ser, z, n))), n=0..62);

%t m = 62;

%t gf = (Cosh[x*z] + Cos[x*z])*z/(1 - E^-z);

%t Denominator[CoefficientList[(gf/.x->1)+O[z]^(m+1),z]*Range[0,m]!] (* _Jean-Fran├žois Alcover_, Jun 04 2019 *)

%Y Cf. A318141 (numerators).

%K nonn,frac

%O 0,3

%A _Peter Luschny_, Aug 19 2018

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Last modified October 28 17:55 EDT 2021. Contains 348329 sequences. (Running on oeis4.)