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%I #21 Dec 25 2023 17:34:10
%S 1,-1,1,0,-10,90,-730,6160,-55900,549900,-5864300,67610400,-839594600,
%T 11186357000,-159300557000,2416003824000,-38894192662000,
%U 662595375078000,-11911522255750000,225382826562400000,-4477959179352100000,93217812901913700000,-2029107997508660900000,46099220630461596000000
%N Imaginary part of Product_{k=0..n} (i-k), where i=sqrt(-1).
%C Shifted version of A009454. - _R. J. Mathar_, May 30 2014
%D Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea Publishing, NY 1953, pp. 561-562, Section 148.
%e Table of n, Product_{k=0..n) (i-k):
%e 0, i
%e 1, -1 - i
%e 2, 3 + i
%e 3, -10
%e 4, 40 - 10*i
%e 5, -190 + 90*i
%e 6, 1050 - 730*i
%e 7, -6620 + 6160*i
%e 8, 46800 - 55900*i
%e 9, -365300 + 549900*i
%e 10, 3103100 - 5864300*i
%e 11, -28269800 + 67610400*i
%e 12, 271627200 - 839594600*i
%p a:= n-> Im(mul(I-j, j=0..n)):
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Jan 03 2021
%o (PARI) a(n) = imag(prod(k=0, n, I-k)); \\ _Michel Marcus_, Jan 03 2021
%Y Cf. A242651, A101686.
%Y A231531 is the same except for signs.
%K sign
%O 0,5
%A _N. J. A. Sloane_, May 29 2014
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