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A242651
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Real part of Product_{k=0..n} (i-k), where i = sqrt(-1).
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3
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0, -1, 3, -10, 40, -190, 1050, -6620, 46800, -365300, 3103100, -28269800, 271627200, -2691559000, 26495469000, -238131478000, 1394099824000, 15194495654000, -936096296850000, 29697351895900000, -819329864480400000, 21683886333440500000, -570263312237604700000, 15145164178973569000000
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea Publishing, NY 1953, pp. 561-562, Section 148.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor((n+1)/2)} (-1)^k*Stirling1(n+1,2*k). - Ammar Khatab, May 23 2021
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EXAMPLE
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Table of n, Product_{k=0..n} (i-k):
0, i
1, -1 - i
2, 3 + i
3, -10
4, 40 - 10*i
5, -190 + 90*i
6, 1050 - 730*i
7, -6620 + 6160*i
8, 46800 - 55900*i
9, -365300 + 549900*i
10, 3103100 - 5864300*i
11, -28269800 + 67610400*i
12, 271627200 - 839594600*i
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MATHEMATICA
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Table[Re[(I - n)*Pochhammer[1 + I - n, n]], {n, 0, 25}] (* Vaclav Kotesovec, May 23 2021 *)
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PROG
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(PARI) a(n) = real(prod(k=0, n, I-k)); \\ Michel Marcus, Jan 03 2021
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CROSSREFS
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A231531 is the same except for signs.
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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