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