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a(n) = denominator(n!*[z^n](z*(exp(z)+2*exp(-(1/2)*z)*cos((1/2)*z* 3^(1/2)))/(1-exp(-z)))).
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%I #11 Aug 19 2018 14:22:54

%S 1,2,2,1,10,1,14,1,10,1,22,1,910,1,10,1,170,1,1330,1,110,1,230,1,910,

%T 1,2,1,290,1,4774,1,1870,1,2,1,639730,1,10,1,4510,1,33110,1,230,1,470,

%U 1,15470,1,374,1,5830,1,2926,1,290,1,118,1,18928910,1,110,1

%N a(n) = denominator(n!*[z^n](z*(exp(z)+2*exp(-(1/2)*z)*cos((1/2)*z* 3^(1/2)))/(1-exp(-z)))).

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

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

%p gf := z*(exp(z)+2*exp(-(1/2)*z)*cos((1/2)*z*sqrt(3)))/(1-exp(-z));

%p ser := series(gf, z, 70): seq(denom(n!*coeff(ser, z, n)),n=0..63);

%Y Cf. A306148 (numerator).

%K nonn,frac

%O 0,2

%A _Peter Luschny_, Aug 19 2018