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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

Richard Ehrenborg and Margaret A. Readdy, Sheffer posets and r-signed permutations, Annales des Sciences Mathématiques du Québec {\bf 19} (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.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))

[A007286(n) for n in (0..17)] # Peter Luschny, Apr 28 2013

CROSSREFS

Cf. A006873, A007289, A225109, A002438 (bisection?).

Sequence in context: A175151 A121750 A143341 * A099032 A277489 A094652

Adjacent sequences:  A007283 A007284 A007285 * A007287 A007288 A007289

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and Simon Plouffe

STATUS

approved

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Last modified March 30 20:18 EDT 2017. Contains 284302 sequences.