A130653 - OEIS

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A130653

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

1, 1, 17, 929569, 129848163681107301953, 7724760729208487305545342963324697288405380586579904269441, 357302767470032900576643605538835088084055212588960920085261795996340330997333306469144562500392344758421560010463942134842407723273904635849262137252097 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,3`
	COMMENTS	`Odd terms in A002430(n) correspond to the indices that are the powers of 2.`
	LINKS	`Eric Weisstein's World of Mathematics, Tangent.`
	FORMULA	`a(n) = Numerator[ Abs[ 2^(2^n)(2^(2^n)-1)/(2^n)! * BernoulliB[ 2^n ] ] ]. a(n) = A002430(2^(n-1)).`
	EXAMPLE	`tan(x) = x + 2 x^3/3! + 16 x^5/5! + 272 x^7/7! + ... = 1x + 1/3x^3 + 2/15x^5 + 17/315x^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.`
	MATHEMATICA	`Table[ Numerator[ Abs[ 2^(2^n)(2^(2^n)-1)/(2^n)! * BernoulliB[ 2^n ] ] ], {n, 1, 8} ]`
	CROSSREFS	`Cf. A002430 = Numerators in Taylor series for tan(x). Also from Taylor series for tanh(x). Cf. A001469, A002425, A046990, A089171, A110501, A036968.` `Sequence in context: A051157 A177918 A177816 * A125039 A125041 A013806` `Adjacent sequences: A130650 A130651 A130652 * A130654 A130655 A130656`
	KEYWORD	`nonn`
	AUTHOR	`Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 20 2007`

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Last modified February 17 19:13 EST 2012. Contains 206085 sequences.