# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a007286 Showing 1-1 of 1 %I A007286 M3945 #48 Mar 15 2020 14:17:59 %S A007286 1,1,5,26,205,1936,22265,297296,4544185,78098176,1491632525, %T A007286 31336418816,718181418565,17831101321216,476768795646785, %U A007286 13658417358350336,417370516232719345,13551022195053101056 %N A007286 E.g.f.: (sin x + cos 2x) / cos 3x. %C A007286 Arises in the enumeration of alternating 3-signed permutations. %D A007286 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A007286 Vincenzo Librandi, Table of n, a(n) for n = 0..200 %H A007286 R. Ehrenborg and M. A. Readdy, Sheffer posets and r-signed permutations, Preprint, 1994. (Annotated scanned copy) %H A007286 Richard Ehrenborg and Margaret A. Readdy, Sheffer posets and r-signed permutations, Annales des Sciences Mathématiques du Québec 19:2 (1995), 173-196. %F A007286 a(n) = Re(2*((1-I)/(1+I))^n*(1+sum_{j=0..n}(binomial(n,j)*Li_{-j}(I)*3^j))). - _Peter Luschny_, Apr 28 2013 %F A007286 a(n) ~ n! * 2^(n+1)*3^n/Pi^(n+1). - _Vaclav Kotesovec_, Jun 15 2013 %t A007286 mx = 17; Range[0, mx]! CoefficientList[ Series[ (Sin[x] + Cos[2x])/Cos[3 x], {x, 0, mx}], x] (* _Robert G. Wilson v_, Apr 28 2013 *) %o A007286 (PARI) x='x+O('x^66); Vec(serlaplace((sin(x)+cos(2*x))/cos(3*x))) \\ _Joerg Arndt_, Apr 28 2013 %o A007286 (Sage) %o A007286 from mpmath import mp, polylog, re %o A007286 mp.dps = 32; mp.pretty = True %o A007286 def aperm3(n): return 2*((1-I)/(1+I))^n*(1+add(binomial(n,j)*polylog(-j,I)*3^j for j in (0..n))) %o A007286 def A007286(n) : return re(aperm3(n)) %o A007286 [int(A007286(n)) for n in (0..17)] # _Peter Luschny_, Apr 28 2013 %Y A007286 Cf. A006873, A007289, A225109, A002438 (bisection?). %K A007286 nonn %O A007286 0,3 %A A007286 _N. J. A. Sloane_ and _Simon Plouffe_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE