A121626 Real part of (1 + n*i)^n, where i=sqrt(-1).
1, 1, -3, -26, 161, 2876, -27755, -740536, 9722113, 343603216, -5707904499, -250756091552, 5039646554593, 264489160965056, -6237995487261915, -380574552503498624, 10303367499652761601, 716309568462681538816, -21891769059478538933603
Offset: 0
Examples
a(4) = 161 since (1 + 4i)^4 = (161 - 240i).
Programs
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Mathematica
a[n_] := Re[(1 + n*I)^n]; Array[a, 18] (* Robert G. Wilson v, Aug 17 2006 *)
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PARI
a(n) = real((1 + n*I)^n); \\ Michel Marcus, Feb 14 2024
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Python
from math import comb def A121626(n): return sum(comb(n,j)*n**j*(-1 if j&2 else 1) for j in range(0,n+1,2)) # Chai Wah Wu, Feb 15 2024
Formula
a(n) = (1/2) * ( (i+n)^n + (i-n)^n ) * i^(n*(2*n+1)). - Bruno Berselli, Jan 28 2014
a(n) = Sum_{j=0..floor(n/2)} binomial(n,2j)*n^(2j)*(-1)^j. - Chai Wah Wu, Feb 15 2024
Extensions
More terms from Robert G. Wilson v, Aug 17 2006