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The number of self-inverse Boolean functions of n variables.
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%I #8 Aug 04 2017 15:24:02

%S 1,2,10,764,46206736,22481059424730751232,

%T 135041388282796985771272553475002706667235246080,

%U 5391278204075391354568253023229655921370142671388586075937736698667444395805138812903649656844450530044101525504

%N The number of self-inverse Boolean functions of n variables.

%F a(n) = Sum_{k=0..2^(n-1)} (2^n)!/((2^n-2*k)! * k! * 2^k).

%F a(n) = A000085(2^n).

%t Table[Sum[(2^n)!/((2^n - 2 k)!*k!*2^k), {k, 0, 2^(n - 1)}], {n, 0, 7}] (* _Michael De Vlieger_, Aug 04 2017 *)

%o (PARI) a(n) = sum(k=0, 2^(n-1), (2^n)!/((2^n-2*k)!*k!*2^k)) \\ _Felix Fröhlich_, Aug 04 2017

%Y Cf. A000722 (invertible Boolean functions).

%K nonn

%O 0,2

%A _Sean A. Irvine_, Aug 04 2017