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

1, -1, 1, 0, -10, 90, -730, 6160, -55900, 549900, -5864300, 67610400, -839594600, 11186357000, -159300557000, 2416003824000, -38894192662000, 662595375078000, -11911522255750000, 225382826562400000, -4477959179352100000, 93217812901913700000, -2029107997508660900000, 46099220630461596000000

Offset: 0

Author

N. J. A. Sloane, May 29 2014

Keywords

• sign

Comments

Shifted version of A009454. - 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. A009454.

Cf. A242651, A101686.

A231531 is the same except for signs.

Programs

Maple

a:= n-> Im(mul(I-j, j=0..n)):
seq(a(n), n=0..25);  # Alois P. Heinz, Jan 03 2021

PARI

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