A007286 E.g.f.: (sin x + cos 2x) / cos 3x. (Formerly M3945)

1, 1, 5, 26, 205, 1936, 22265, 297296, 4544185, 78098176, 1491632525, 31336418816, 718181418565, 17831101321216, 476768795646785, 13658417358350336, 417370516232719345, 13551022195053101056

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: A303970 A366215 A348206 * A305201 A099032 A277489

Adjacent sequences: A007283 A007284 A007285 * A007287 A007288 A007289

Keyword

nonn

Author

N. J. A. Sloane and Simon Plouffe

Status

approved