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 A000708 a(n) = E(n+1)-2E(n), where E(i) is the Euler number A000111(i). (Formerly M4188 N1745) 4

%I M4188 N1745

%S -1,-1,0,1,6,29,150,841,5166,34649,252750,1995181,16962726,154624469,

%T 1505035350,15583997521,171082318686,1985148989489,24279125761950,

%U 312193418011861,4210755676649046,59445878286889709,876726137720576550

%N a(n) = E(n+1)-2E(n), where E(i) is the Euler number A000111(i).

%C a(n) mod 10 for n>=2 is the periodic sequence repeat: 0, 1, 6, 9.

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.

%D E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 113.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H M. E. Estanave, <a href="http://smf4.emath.fr/Publications/Bulletin/30/html/">Sur les coefficients des développements en séries de tang x, séc x et d'autres fonctions. Caractères de périodicité que présentent les chiffres des unités de ces coefficients</a>, Bulletin de la S.M.F., 30 (1902), pp. 220-226.

%F E.g.f. 2*(1+x) + (1-2*cos(x))/(1-sin(x)).

%p seq(i!*coeff(series(((tan(t)+sec(t))^2-4*(tan(t)+sec(t)))/2,t,35),t,i),i=2..24);

%o (PARI) x='x+O('x^99); Vec(serlaplace(2*(1+x)+(1-2*cos(x))/(1-sin(x))))

%Y Apart from initial terms, equals (1/2)*A001758. A diagonal of A008970.

%K sign

%O 0,5

%A _N. J. A. Sloane_.

%E More terms, Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 3/12/01

%E Corrected and extended by _T. D. Noe_, Oct 25 2006

%E Edited by _N. J. A. Sloane_, Aug 27 2012

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Last modified May 24 20:01 EDT 2013. Contains 225630 sequences.