cp's OEIS Frontend

A367518 Numerators of even-numbered Maclaurin coefficients of sqrt(tan(x)/x).

%I A367518 #19 Mar 28 2025 07:15:33
%S A367518 1,1,19,55,11813,2117,64604977,263101079,1768132943,9606907803497,
%T A367518 158812278992229461,9112944418860287,2117852079027536379043,
%U A367518 27841657661565660151,909416652267282749299777,26176589384334728915393123,22901449589921151647801250738173,514908297269179169530303586629
%N A367518 Numerators of even-numbered Maclaurin coefficients of sqrt(tan(x)/x).
%C A367518 Numerators of Maclaurin coefficients of sqrt(tan(sqrt(x)))/x^(1/4).
%H A367518 Robert Israel, <a href="/A367518/b367518.txt">Table of n, a(n) for n = 0..241</a>
%F A367518 sqrt(tan(x)/x) = Sum_{k=0..oo} a(k)/A367519(k) * x^(2*k).
%F A367518 a(n) = numerator(b(n)), where b(n) = Sum_{j=2..n+1} b(n+1-j)*Bernoulli(2*j)*((-4)^j-(-16)^j)*((3*j-3)/(2*n)-1)/(2*j)!, with b(0)=1. - _Tani Akinari_, Feb 26 2025
%e A367518 sqrt(tan(x)/x) = 1 + (1/6) * x^2 + (19/360) * x^4 + (55/3024) * x^6 + ...
%p A367518 S:= series(sqrt(tan(x)/x), x, 41):
%p A367518 seq(numer(coeff(S,x,i)),i=0..40,2);
%o A367518 (Maxima) b[n]:=if n=0 then 1 else sum(b[n+1-j]*bern(2*j)*((-4)^j-(-16)^j)*((3*j-3)/(2*n)-1)/(2*j)!,j,2,n+1)$ a(n):=num(b[n])$ makelist(a(n),n,0,30); /* _Tani Akinari_, Feb 26 2025 */
%o A367518 (PARI) my(x='x+O('x^40), v=apply(numerator, Vec(sqrt(tan(x)/x)))); vector(#v\2, k, v[2*k-1]) \\ _Michel Marcus_, Feb 26 2025
%Y A367518 Cf. A002430, A367519.
%K A367518 nonn,frac
%O A367518 0,3
%A A367518 _Robert Israel_, Nov 21 2023