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A242651 Real part of Product_{k=0..n} (i-k), where i = sqrt(-1).

%I A242651 #29 May 23 2021 02:58:46
%S A242651 0,-1,3,-10,40,-190,1050,-6620,46800,-365300,3103100,-28269800,
%T A242651 271627200,-2691559000,26495469000,-238131478000,1394099824000,
%U A242651 15194495654000,-936096296850000,29697351895900000,-819329864480400000,21683886333440500000,-570263312237604700000,15145164178973569000000
%N A242651 Real part of Product_{k=0..n} (i-k), where i = sqrt(-1).
%C A242651 Shifted version of A003703. - _R. J. Mathar_, May 30 2014
%D A242651 Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea Publishing, NY 1953, pp. 561-562, Section 148.
%F A242651 a(n) = Sum_{k=0..floor((n+1)/2)} (-1)^k*Stirling1(n+1,2*k). - _Ammar Khatab_, May 23 2021
%e A242651 Table of n, Product_{k=0..n} (i-k):
%e A242651    0,         i
%e A242651    1,        -1 -           i
%e A242651    2,         3 +           i
%e A242651    3,       -10
%e A242651    4,        40 -        10*i
%e A242651    5,      -190 +        90*i
%e A242651    6,      1050 -       730*i
%e A242651    7,     -6620 +      6160*i
%e A242651    8,     46800 -     55900*i
%e A242651    9,   -365300 +    549900*i
%e A242651   10,   3103100 -   5864300*i
%e A242651   11, -28269800 +  67610400*i
%e A242651   12, 271627200 - 839594600*i
%t A242651 Table[Re[(I - n)*Pochhammer[1 + I - n, n]], {n, 0, 25}] (* _Vaclav Kotesovec_, May 23 2021 *)
%o A242651 (PARI) a(n) = real(prod(k=0, n, I-k)); \\ _Michel Marcus_, Jan 03 2021
%Y A242651 Cf. A003703, A242652, A101686.
%Y A242651 A231531 is the same except for signs.
%K A242651 sign
%O A242651 0,3
%A A242651 _N. J. A. Sloane_, May 29 2014