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A105750 RE(Product{k=0..n, 1+kI}), I=sqrt(-1). 5
1, 1, -1, -10, -10, 190, 730, -6620, -55900, 365300, 5864300, -28269800, -839594600, 2691559000, 159300557000, -238131478000, -38894192662000, -15194495654000, 11911522255750000, 29697351895900000, -4477959179352100000, -21683886333440500000, 2029107997508660900000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Define u(n) as in A220448 and set f(n) = u(n)*f(n-1) for n>=2, with f(1)=1 (this defines A220449). Then a(0)=1; a(n) = (-1)^(n+1)*f(n) for n >= 1. - N. J. A. Sloane, Dec 22 2012

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..100

V. H. Moll, An arithmetic conjecture on a sequence of arctangent sums, 2012, see f_n.

FORMULA

a(n)=RE(Product{k=0..n, 1-kI}).

Conjecture: a(n) -3*a(n-1) +(n^2-n+3)*a(n-2) +(-n^2+4*n-5)*a(n-3)=0. - R. J. Mathar, May 23 2014

MAPLE

A105750 := proc(n)

    mul(1-k*I, k=0..n) ;

    Re(%) ;

end proc: # R. J. Mathar, Jan 04 2013

CROSSREFS

Cf. A009454, A003703, A105751, A220448, A220449.

Sequence in context: A287600 A047817 A065243 * A220449 A318968 A288051

Adjacent sequences:  A105747 A105748 A105749 * A105751 A105752 A105753

KEYWORD

easy,sign

AUTHOR

Paul Barry, Apr 18 2005

EXTENSIONS

Corrected by N. J. A. Sloane, Nov 05 2005

STATUS

approved

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Last modified May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)