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A242652 Imaginary part of Product_{k=0..n} (i-k), where i=sqrt(-1).

%I A242652 #27 Nov 09 2024 04:17:19
%S A242652 1,-1,1,0,-10,90,-730,6160,-55900,549900,-5864300,67610400,-839594600,
%T A242652 11186357000,-159300557000,2416003824000,-38894192662000,
%U A242652 662595375078000,-11911522255750000,225382826562400000,-4477959179352100000,93217812901913700000,-2029107997508660900000,46099220630461596000000
%N A242652 Imaginary part of Product_{k=0..n} (i-k), where i=sqrt(-1).
%C A242652 Shifted version of A009454. - _R. J. Mathar_, May 30 2014
%D A242652 Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea Publishing, NY 1953, pp. 561-562, Section 148.
%e A242652 Table of n, Product_{k=0..n} (i-k):
%e A242652    0, i
%e A242652    1, -1 - i
%e A242652    2, 3 + i
%e A242652    3, -10
%e A242652    4, 40 - 10*i
%e A242652    5, -190 + 90*i
%e A242652    6, 1050 - 730*i
%e A242652    7, -6620 + 6160*i
%e A242652    8, 46800 - 55900*i
%e A242652    9, -365300 + 549900*i
%e A242652   10, 3103100 - 5864300*i
%e A242652   11, -28269800 + 67610400*i
%e A242652   12, 271627200 - 839594600*i
%p A242652 a:= n-> Im(mul(I-j, j=0..n)):
%p A242652 seq(a(n), n=0..25);  # _Alois P. Heinz_, Jan 03 2021
%o A242652 (PARI) a(n) = imag(prod(k=0, n, I-k)); \\ _Michel Marcus_, Jan 03 2021
%Y A242652 Cf. A009454.
%Y A242652 Cf. A242651, A101686.
%Y A242652 A231531 is the same except for signs.
%K A242652 sign
%O A242652 0,5
%A A242652 _N. J. A. Sloane_, May 29 2014