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 A121626 Real part of (1 + n*i)^n, where i=sqrt(-1). 1

%I

%S 1,-3,-26,161,2876,-27755,-740536,9722113,343603216,-5707904499,

%T -250756091552,5039646554593,264489160965056,-6237995487261915,

%U -380574552503498624,10303367499652761601,716309568462681538816,-21891769059478538933603

%N Real part of (1 + n*i)^n, where i=sqrt(-1).

%C This sequence is a companion to A115415: real part of (n + i)^n.

%F a(n) = (1/2) * ( (i+n)^n + (i-n)^n ) * i^(n*(2*n+1)). [_Bruno Berselli_, Jan 28 2014]

%e a(4) = 161 since (1 + 4i)^4 = (161 - 240i).

%t f[n_] := Re[(1 + n*I)^n]; Array[f, 18] (* _Robert G. Wilson v_, Aug 17 2006 *)

%t Table[(1/2) ((I + n)^n + (I - n)^n) I^(n (2 n + 1)), {n, 20}] (* _Bruno Berselli_, Jan 28 2014 *)

%Y Cf. A115415.

%K sign,easy

%O 1,2

%A _Gary W. Adamson_, Aug 12 2006

%E More terms from _Robert G. Wilson v_, Aug 17 2006

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Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)