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%I #11 Apr 22 2020 23:48:15
%S 1,325,44850,3453450,164038875,5019589575,100391791500,1305093289500,
%T 10767019638375,53835098191875,150738274937250,205552193096250,
%U 102776096548125,7905853580625,0,0,0
%N Number of possible plugboard settings for a WWII German Enigma Cipher Machine with n cables.
%C a(n) increases to a maximum at n = 11, then decreases.
%D Andrew Hodges, Alan Turing: the Enigma, Princeton University Press, 2014.
%H A. Ray Miller, <a href="http://dx.doi.org/10.1080/0161-119591883773">The Cryptographic Mathematics of Enigma</a>, Cryptologia, 19 (1995), 65-80.
%H Kalika Prasad and Munesh Kumari, <a href="https://arxiv.org/abs/2004.09982">A review on mathematical strength and analysis of Enigma</a>, arXiv:2004.09982 [cs.CR], 2020.
%H Tony Sale, <a href="http://www.codesandciphers.org.uk/enigma/steckercount.htm">Counting the Possible Plugboard Setting</a>, Codes and Ciphers, Enigma.
%F a(n) = 26! / ((26 - 2n)! n! 2^n) = C(2,26,n) (see A181386).
%t Table[26!/((26 - 2 n)! n! 2^n), {n, 0, 16}]
%Y Cf. A181386.
%K nonn
%O 0,2
%A _Jonathan Sondow_, Dec 28 2015