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 A007286 E.g.f.: (sin x + cos 2x) / cos 3x. (Formerly M3945) 5
 1, 1, 5, 26, 205, 1936, 22265, 297296, 4544185, 78098176, 1491632525, 31336418816, 718181418565, 17831101321216, 476768795646785, 13658417358350336, 417370516232719345, 13551022195053101056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Arises in the enumeration of alternating 3-signed permutations. REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 R. Ehrenborg and M. A. Readdy, Sheffer posets and r-signed permutations, Preprint, 1994. (Annotated scanned copy) Richard Ehrenborg and Margaret A. Readdy, Sheffer posets and r-signed permutations, Annales des Sciences Mathématiques du Québec 19:2 (1995), 173-196. FORMULA 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 a(n) ~ n! * 2^(n+1)*3^n/Pi^(n+1). - Vaclav Kotesovec, Jun 15 2013 MATHEMATICA 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 *) PROG (PARI) x='x+O('x^66); Vec(serlaplace((sin(x)+cos(2*x))/cos(3*x))) \\ Joerg Arndt, Apr 28 2013 (Sage) from mpmath import mp, polylog, re mp.dps = 32; mp.pretty = True 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))) def A007286(n) : return re(aperm3(n)) [int(A007286(n)) for n in (0..17)] # Peter Luschny, Apr 28 2013 CROSSREFS Cf. A006873, A007289, A225109, A002438 (bisection?). Sequence in context: A121750 A143341 A303970 * A305201 A099032 A277489 Adjacent sequences:  A007283 A007284 A007285 * A007287 A007288 A007289 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 20 23:46 EDT 2021. Contains 343143 sequences. (Running on oeis4.)