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Odd terms in A002430 = numerators in Taylor series for tan(x).
0

%I #2 Mar 31 2012 13:20:36

%S 1,1,17,929569,129848163681107301953,

%T 7724760729208487305545342963324697288405380586579904269441,

%U 357302767470032900576643605538835088084055212588960920085261795996340330997333306469144562500392344758421560010463942134842407723273904635849262137252097

%N Odd terms in A002430 = numerators in Taylor series for tan(x).

%C Odd terms in A002430(n) correspond to the indices that are the powers of 2.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Tangent.html">Tangent</a>.

%F a(n) = Numerator[ Abs[ 2^(2^n)(2^(2^n)-1)/(2^n)! * BernoulliB[ 2^n ] ] ]. a(n) = A002430(2^(n-1)).

%e tan(x) = x + 2 x^3/3! + 16 x^5/5! + 272 x^7/7! + ... = 1*x + 1/3*x^3 + 2/15*x^5 + 17/315*x^7 + 62/2835*x^9 + O(x^10).

%e A002430(n) begins {1, 1, 2, 17, 62, 1382, 21844, 929569, 6404582, 443861162, 18888466084, 113927491862, 58870668456604, 8374643517010684, 689005380505609448, 129848163681107301953, ...}.

%e Thus a(1) = 1, a(2) = 1, a(3) = 17, a(4) = 929569, a(5) = 129848163681107301953.

%t Table[ Numerator[ Abs[ 2^(2^n)(2^(2^n)-1)/(2^n)! * BernoulliB[ 2^n ] ] ], {n,1,8} ]

%Y Cf. A002430 = Numerators in Taylor series for tan(x). Also from Taylor series for tanh(x). Cf. A001469, A002425, A046990, A089171, A110501, A036968.

%K nonn

%O 1,3

%A _Alexander Adamchuk_, Jun 20 2007