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 A009123 Expansion of e.g.f.: cosh(log(1+sin(x))). 3
 1, 0, 1, -3, 8, -30, 136, -693, 3968, -25260, 176896, -1351383, 11184128, -99680490, 951878656, -9695756073, 104932671488, -1202439837720, 14544442556416, -185185594118763, 2475749026562048, -34674437196568950 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS |a(n)| = number of even alternating permutations on n letters (offset 1). - Vladeta Jovovic, May 20 2007 LINKS G. C. Greubel, Table of n, a(n) for n = 0..250 FORMULA a(2*n) = (1/2)*A000182(n+1); a(2*n+1) = A012007(n+1) = A009567(2*n+1) + 1. G.f.: (1+x/(1+x^2))/2 + 1/2/Q(0) where Q(k) =  1 + (k+1)*x - x^2*(k+1)*(k+2)/2 /Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Mar 12 2013 a(n) ~ n! * n * (-1)^n * (2/Pi)^(n+2). - Vaclav Kotesovec, Jan 22 2015 MATHEMATICA CoefficientList[Series[(1 + (1 + Sin[x])^2)/(2*(1 + Sin[x])), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *) PROG (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+sin(x))))) \\ G. C. Greubel, Jul 26 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+Sin(x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 26 2018 CROSSREFS Cf. A000111. Sequence in context: A096161 A161779 A074501 * A066764 A059171 A261766 Adjacent sequences:  A009120 A009121 A009122 * A009124 A009125 A009126 KEYWORD sign,easy AUTHOR EXTENSIONS Extended with signs by Olivier Gérard, Mar 15 1997 STATUS approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)