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a(n) = Im([n]_{1+i}!), where [n]_q! is the q-factorial, i = sqrt(-1).
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%I #6 Sep 14 2016 07:51:58

%S 0,0,1,8,5,-220,1895,-9140,-302175,-2778300,-95631825,-10071428100,

%T -236788407375,57706241794500,-7412904844112625,525300693117661500,

%U 348922898045520800625,55166584329677385922500,28368558145043150339199375,46873210124734003815040957500

%N a(n) = Im([n]_{1+i}!), where [n]_q! is the q-factorial, i = sqrt(-1).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/q-Factorial.html">q-Factorial</a>.

%p a:= n-> Im(mul(((1+I)^j-1)/((1+I)-1), j=1..n)):

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Sep 14 2016

%t Im@Table[QFactorial[n, 1 + I], {n, 0, 20}]

%Y Cf. A275706 (real part), A005329.

%K sign

%O 0,4

%A _Vladimir Reshetnikov_, Sep 13 2016