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Numerators of even-numbered Maclaurin coefficients of sqrt(tan(x)/x).
2

%I #9 Nov 22 2023 22:22:44

%S 1,1,19,55,11813,2117,64604977,263101079,1768132943,9606907803497,

%T 158812278992229461,9112944418860287,2117852079027536379043,

%U 27841657661565660151,909416652267282749299777,26176589384334728915393123,22901449589921151647801250738173,514908297269179169530303586629

%N Numerators of even-numbered Maclaurin coefficients of sqrt(tan(x)/x).

%C Numerators of Maclaurin coefficients of sqrt(tan(sqrt(x))/x^(1/4).

%H Robert Israel, <a href="/A367518/b367518.txt">Table of n, a(n) for n = 0..241</a>

%F sqrt(tan(x)/x) = Sum_{k=0..oo} a(k)/A367519(k) * x^(2*k).

%e sqrt(tan(x)/x) = 1 + (1/6) * x^2 + (19/360) * x^4 + (55/3024) * x^6 + ...

%p S:= series(sqrt(tan(x)/x), x, 41):

%p seq(numer(coeff(S,x,i)),i=0..40,2);

%Y Cf. A002430, A367519.

%K nonn,frac

%O 0,3

%A _Robert Israel_, Nov 21 2023