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

0, -1, 3, -10, 40, -190, 1050, -6620, 46800, -365300, 3103100, -28269800, 271627200, -2691559000, 26495469000, -238131478000, 1394099824000, 15194495654000, -936096296850000, 29697351895900000, -819329864480400000, 21683886333440500000, -570263312237604700000, 15145164178973569000000

Offset: 0

Author

N. J. A. Sloane, May 29 2014

Keywords

• sign

Comments

Shifted version of A003703. - R. J. Mathar, May 30 2014

Examples

			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
		

References

• Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea Publishing, NY 1953, pp. 561-562, Section 148.

Crossrefs

Cf. A003703, A242652, A101686.

A231531 is the same except for signs.

Programs

Mathematica

Table[Re[(I - n)*Pochhammer[1 + I - n, n]], {n, 0, 25}] (* Vaclav Kotesovec, May 23 2021 *)

PARI

a(n) = real(prod(k=0, n, I-k)); \\ Michel Marcus, Jan 03 2021

Formula

a(n) = Sum_{k=0..floor((n+1)/2)} (-1)^k*Stirling1(n+1,2*k). - Ammar Khatab, May 23 2021