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A006873 Number of alternating 4-signed permutations.
(Formerly M4430)
5
1, 1, 7, 47, 497, 6241, 95767, 1704527, 34741217, 796079041, 20273087527, 567864586607, 17352768515537, 574448847467041, 20479521468959287, 782259922208550287, 31872138933891307457, 1379749466246228538241, 63243057486503656319047, 3059895336952604166395567 (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

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, 19 (1995), 173-196.

FORMULA

E.g.f.: (sin(x) + cos(3x)) / cos(4x). - M. F. Hasler, Apr 28 2013

a(n) = Re(2*((1-I)/(1+I))^n*(1+sum_{j=0..n}(binomial(n,j)*Li_{-j}(I)* 4^j))). - Peter Luschny, Apr 29 2013

a(n) ~ sqrt(2-sqrt(2)) * 2^(3*n+3/2) * n^(n+1/2) / (Pi^(n+1/2) * exp(n)). - Vaclav Kotesovec, Feb 25 2014

MAPLE

per4 := proc(n) local j; 2*((1-I)/(1+I))^n*(1+add(binomial(n, j)* polylog(-j, I)*4^j, j=0..n)) end: A006873 := n -> Re(per4(n));

seq(A006873(i), i=0..11); # Peter Luschny, Apr 29 2013

MATHEMATICA

mx = 17; Range[0, mx]! CoefficientList[ Series[ (Sin[x] + Cos[3x])/Cos[4x], {x, 0, mx}], x] (* Robert G. Wilson v, Apr 28 2013 *)

PROG

(PARI) x='x+O('x^66); Vec(serlaplace((sin(x)+cos(3*x))/cos(4*x))) \\ Joerg Arndt, Apr 28 2013

CROSSREFS

Cf. A007286, A007289, A225109.

Sequence in context: A218761 A173772 A178002 * A228695 A268063 A015097

Adjacent sequences:  A006870 A006871 A006872 * A006874 A006875 A006876

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and Simon Plouffe

EXTENSIONS

Added more terms, Joerg Arndt, Apr 28 2013

STATUS

approved

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