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A105751 Imaginary part of Product_{k=0..n} 1+k*I, I=sqrt(-1). 2

%I

%S 0,1,3,0,-40,-90,1050,6160,-46800,-549900,3103100,67610400,-271627200,

%T -11186357000,26495469000,2416003824000,-1394099824000,

%U -662595375078000,-936096296850000,225382826562400000,819329864480400000,-93217812901913700000,-570263312237604700000

%N Imaginary part of Product_{k=0..n} 1+k*I, I=sqrt(-1).

%H Seiichi Manyama, <a href="/A105751/b105751.txt">Table of n, a(n) for n = 0..450</a>

%F a(n) = ((2*n-1)*a(n-1)-(n^2-2*n+2)*n*a(n-2))/(n-1) for n > 1, a(n) = n for n < 2. - _Alois P. Heinz_, Apr 11 2018

%p a:= proc(n) option remember; `if`(n<2, n,

%p ((2*n-1)*a(n-1)-(n^2-2*n+2)*n*a(n-2))/(n-1))

%p end:

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Apr 11 2018

%o (PARI) a(n) = imag(prod(k=0, n, 1+k*I)); \\ _Michel Marcus_, Apr 11 2018

%Y Cf. A003703, A009454, A105750, A231531.

%K easy,sign

%O 0,3

%A _Paul Barry_, Apr 18 2005

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Last modified May 25 12:30 EDT 2019. Contains 323568 sequences. (Running on oeis4.)