A130653 Odd terms in A002430 = numerators in Taylor series for tan(x).

1, 1, 17, 929569, 129848163681107301953, 7724760729208487305545342963324697288405380586579904269441, 357302767470032900576643605538835088084055212588960920085261795996340330997333306469144562500392344758421560010463942134842407723273904635849262137252097

Offset: 1

Author

Alexander Adamchuk, Jun 20 2007

Keywords

• nonn

Comments

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

Examples

			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).
A002430(n) begins {1, 1, 2, 17, 62, 1382, 21844, 929569, 6404582, 443861162, 18888466084, 113927491862, 58870668456604, 8374643517010684, 689005380505609448, 129848163681107301953, ...}.
Thus a(1) = 1, a(2) = 1, a(3) = 17, a(4) = 929569, a(5) = 129848163681107301953.
		

Links

• Eric Weisstein's World of Mathematics, Tangent.

Crossrefs

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

Programs

Mathematica

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

Formula

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