%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