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 A012509 E.g.f.: -log(cos(x)*cos(x)) (even powers only). 3
 0, 2, 4, 32, 544, 15872, 707584, 44736512, 3807514624, 419730685952, 58177770225664, 9902996106248192, 2030847773013704704, 493842960380415967232, 140503203207887919775744, 46238368375619195682947072, 17427925514250338592341622784, 7458815407441059142195019251712 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Of course this is 2*log(sec(x)), so a(n) = 2*A000182(n). LINKS Table of n, a(n) for n=0..17. Tewodros Amdeberhan, Victor H. Moll and Christophe Vignat, A probabilistic interpretation of a sequence related to Narayana Polynomials, arXiv:1202.1203 [math.NT], 2012. See p. 21. Tewodros Amdeberhan, Victor H. Moll and Christophe Vignat, A probabilistic interpretation of a sequence related to Narayana Polynomials, Online Journal of Analytic Combinatorics, Issue 8, 2013. See p. 21. N. J. A. Sloane, Rough notes on Genocchi numbers FORMULA G.f.: 2/Q(0) where Q(k) = 1 + x*(2*k + 1)*(2*k + 2)/( -1 + x*(2*k + 2)*(2*k + 3)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 11 2013 G.f.: (2/G(0) - 1)*sqrt(-x), where G(k)= 2 + 2*sqrt(-x) - 4*x*(k+1)^2/G(k+1); (continued fraction). - Sergei N. Gladkovskii, May 29 2013 G.f.: 2*x*T(0), where T(k) = 1 - (k+1)*(k+2)*x/((k+1)*(k+2)*x - 1/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 15 2013 a(n) ~ 2^(2*n+2) * (2*n-1)! / Pi^(2*n). - Vaclav Kotesovec, Feb 08 2015 E.g.f. (odd powers): y = 2*tan(x). - Stanislav Sykora, Nov 28 2016 EXAMPLE G.f. = x^2+1/6*x^4+2/45*x^6+17/1260*x^8+62/14175*x^10+691/467775*x^12+... MATHEMATICA nn = 20; Table[(CoefficientList[Series[-Log[Cos[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 08 2015 *) CROSSREFS Cf. A000182. Sequence in context: A101460 A304862 A118992 * A062740 A336832 A122214 Adjacent sequences: A012506 A012507 A012508 * A012510 A012511 A012512 KEYWORD nonn AUTHOR Patrick Demichel (patrick.demichel(AT)hp.com) EXTENSIONS Corrected by D. S. McNeil and N. J. A. Sloane, Dec 17 2011 (The signs were wrong and the initial term was missing) STATUS approved

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Last modified July 20 18:59 EDT 2024. Contains 374459 sequences. (Running on oeis4.)