A047686 - OEIS

%I #15 Jan 03 2025 03:16:02

%S 1,3,90,2835,18900,66825,1915538625,127702575,186080895000,

%T 350813659321125,7656647326453125,3018906660144375,

%U 1211517431782539131250,144228265688397515625,564653660170076273671875,84913182070036240111050234375,499921764568178729658131250000

%N Denominators of coefficients in Taylor series for log(tan(x)/x).

%D CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.

%D Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 34, equation 34:6:3 at page 323.

%H Index entries for <a href="/index/Be#Bernoulli">Bernoulli numbers</a> B(2n)

%F A047685(n)/a(n) = 2^(2n) *(2^(2n-1) -1) *abs(B(2n)) / ((2n)! *n).

%e (1/3)*x^2 + (7/90)*x^4 + (62/2835)*x^6 + (127/18900)*x^8 + (146/66825)*x^10 + ...

%t Join[{1},DeleteCases[Denominator[CoefficientList[Series[Log[Tan[x]/x],{x,0,33}],x]],1]] (* _Stefano Spezia_, Jan 03 2025 *)

%Y Cf. A047685, B(2n)= A027641(2n) / A027642(2n).

%K nonn,easy,frac

%O 0,2

%A _N. J. A. Sloane_