This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A040175 #27 Jun 22 2025 09:18:43 %S A040175 3,9,57,318,3090,24666,234879,2381481,26777922,324421053,4265966685 %N A040175 a(n) = n! times probability that an ordered pair of elements of S_n chosen at random (with replacement) generate S_n. %C A040175 Probability is A040173(n)/A040174(n) = a(n)/n!. %C A040175 Note that a(2)=3/2 is not integer. %D A040175 J. D. Dixon, Problem 923 (BCC20.17), Indecomposable permutations and transitive groups, in Research Problems from the 20th British Combinatorial Conference, Discrete Math., 308 (2008), 621-630. %H A040175 L. Babai, <a href="http://dx.doi.org/10.1016/0097-3165(89)90068-X">The probability of generating the symmetric group</a>, J. Combin. Theory, A52 (1989), 148-153. %H A040175 J. D. Dixon, <a href="http://dx.doi.org/10.1007/BF01110210">The probability of generating the symmetric group</a>, Math. Z. 110 (1969) 199-205. %H A040175 T. Łuczak and L. Pyber, <a href="http://dx.doi.org/10.1017/S0963548300000869">On random generation of the symmetric group</a>, Combin. Probab. Comput., 2 (1993), 505-512. %H A040175 A. Maroti and C. M. Tamburini, <a href="http://dx.doi.org/10.1007/s00013-010-0216-z">Bounds for the probability of generating the symmetric and alternating groups</a>, Arch. Math. (Basel), 96 (2011), 115-121. %F A040175 a(n) = A071605(n)/n!. %e A040175 Probabilities for n=1,2,3,... are 1, 3/4, 1/2, 3/8, 19/40, ... %Y A040175 Cf. A040173, A040174, A071605, A135474. %K A040175 nonn,more,nice %O A040175 3,1 %A A040175 _Dan Hoey_ %E A040175 Edited by _Max Alekseyev_, Jan 28 2012 %E A040175 a(10)-a(13) from _Stephen A. Silver_, Feb 21 2013