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 A003710 Expansion of e.g.f. cos(tan(x)) (even powers only). (Formerly M4453) 6
 1, -1, -7, -97, -2063, -53409, -752343, 166831871, 43685848289, 9398558916159, 2116926930779225, 524586454143030495, 144620290378876829905, 44287070229737735633567, 14954349885478653319004041 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..100 FORMULA a(n) = 2 * Sum_{m=0..n} ( Sum_{j=2*m..2*n} binomial(j-1,2*m-1) * j! * 2^(2*n-j-1) * (-1)^(n+j) * Stirling2(2*n,j) )/(2*m)!, n>0, a(0)=1. - Vladimir Kruchinin, Jun 29 2011 MATHEMATICA nn = 20; Table[(CoefficientList[Series[Cos[Tan[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 16 2015 *) PROG (Maxima) a(n):=if n=0 then 1 else 2*sum((sum(binomial(j-1, 2*m-1)*j!*2^(2*n-j-1)*(-1)^(n+j)*stirling2(2*n, j), j, 2*m, 2*n))/(2*m)!, m, 0, n); /* Vladimir Kruchinin, Jun 28 2011 */ (PARI) my(x='x+O('x^30)); select(x->x, Vec(serlaplace(cos(tan(x))))) \\ Michel Marcus, Oct 02 2021 CROSSREFS Cf. A003709, A003711. Sequence in context: A305137 A132061 A013521 * A027837 A174315 A046908 Adjacent sequences: A003707 A003708 A003709 * A003711 A003712 A003713 KEYWORD sign AUTHOR STATUS approved

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Last modified December 5 06:15 EST 2022. Contains 358578 sequences. (Running on oeis4.)