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a(n) = A275706(n)^2 + A276688(n)^2 = [n]_{1+i}! * [n]_{1-i}!, where [n]_q! is the q-factorial, i = sqrt(-1).
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%I #4 Sep 17 2016 00:20:08

%S 1,1,5,65,1625,66625,4330625,489360625,110106140625,52961053640625,

%T 54285079981640625,114704374001206640625,484625980155098056640625,

%U 4032572780870570929306640625

%N a(n) = A275706(n)^2 + A276688(n)^2 = [n]_{1+i}! * [n]_{1-i}!, where [n]_q! is the q-factorial, i = sqrt(-1).

%F a(n) = |[n]_{1+i}!|^2.

%F a(n+1)/a(n) = 4*A038505(n) + 1.

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

%Y Cf. A275706, A276688, A038505.

%K nonn

%O 0,3

%A _Vladimir Reshetnikov_, Sep 16 2016