A225845 - OEIS

A225845

Numerator of c(n) = 2^(2*n)*(2^(2*n) - 1)/(2*n)!, a coefficient used in the expansion of tan(x) as Sum_{n>=1} c(n)*|Bernoulli(2*n)|*x^(2*n-1).

%I #17 Sep 08 2022 08:46:05

%S 0,6,10,28,34,1364,52,43688,8738,5548,5084,11184808,964,178956968,

%T 143165576,24790576,33686018,22906492244,1177636,733007751848,

%U 10115684,79783156664,407934748856,375299968947536,16173237188,8804691353608,2401919801264264

%N Numerator of c(n) = 2^(2*n)*(2^(2*n) - 1)/(2*n)!, a coefficient used in the expansion of tan(x) as Sum_{n>=1} c(n)*|Bernoulli(2*n)|*x^(2*n-1).

%D George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 63.

%H Vincenzo Librandi, <a href="/A225845/b225845.txt">Table of n, a(n) for n = 0..300</a>

%t Table[2^(2*n)*(2^(2*n)-1)/(2*n)! // Numerator, {n, 0, 30}]

%o (Magma) [Numerator(2^(2*n)*(2^(2*n)-1)/Factorial(2*n)): n in [0..30]]; // _Vincenzo Librandi_, Jul 17 2013

%Y Cf. A225846 (denominators), A000367, A002445, A002430, A036279.

%K nonn,frac,easy

%O 0,2

%A _Jean-François Alcover_, May 17 2013