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%I A282132 #15 Feb 19 2017 13:51:29
%S A282132 0,1,3,6,30,300,2100,11760,105840,1421280,15634080,147692160,
%T A282132 1919998080,33106993920,496604908800,6638004172800,112846070937600,
%U A282132 2386916704972800,45351417394483200,785383247480832000,16493048197097472000,413938002507853824000
%N A282132 Imaginary part of n!*Sum_{k=1..n} i^(k-1)/k, where i is sqrt(-1).
%H A282132 Daniel Suteu, <a href="/A282132/b282132.txt">Table of n, a(n) for n = 1..100</a>
%F A282132 a(n) ~ log(sqrt(2)) * n!.
%F A282132 a(1) = 0, a(n+1) = a(n)*(n+1) + n!*sin(Pi*n/2).
%e A282132 For n=5, a(5) = 30, which is the imaginary part of 5!*(1/1 + i/2 - 1/3 - i/4 + 1/5) = 104+30*i.
%o A282132 (PARI) a(n) = imag(n!*sum(k=1, n, I^(k-1)/k));
%Y A282132 The corresponding real part is A281964.
%Y A282132 Cf. A016655, A024167.
%K A282132 nonn
%O A282132 1,3
%A A282132 _Daniel Suteu_, Feb 06 2017

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