

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
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OFFSET

0,4


COMMENTS

Define u(n) as in A220448 and set f(n) = u(n)*f(n1) 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, 1kI}).
Conjecture: a(n) 3*a(n1) +(n^2n+3)*a(n2) +(n^2+4*n5)*a(n3)=0.  R. J. Mathar, May 23 2014


MAPLE

A105750 := proc(n)
mul(1k*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



