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 A132431 #19 Sep 13 2023 08:30:06
%S A132431 0,2,9,88,1385,24336,466753,9906688,233522577,6093136000,174912502721,
%T A132431 5487091383456,186891076515481,6870622015481056,271195480556337345,
%U A132431 11440127985767481856,513639921634424850977,24455974520989478444544,1230835712617872016215265
%N A132431 For n>0, let B_n be the subsemigroup of the full transformation monoid on the n-set [n] generated by the following functions: Let x be a certain element in [n]. Now the generators of B are those functions which map either x to any distinct element y in [n] leaving all the other elements fixed, or y to x leaving all the other elements fixed. Then a(n) = number of elements in B_n.
%C A132431 Let b(n)=n^n be the cardinality of the full transformation monoid. The sequence of quotients a(n)/b(n) converges to 1-1/e.
%D A132431 S. Bogner, Eine Praesentation der Halbgruppe der singularen zyklisch-monotonen Abbildungen UND eine von Idempotenten erzeugte Unterhalbgruppe von T_n (Studienarbeit in Informatik, Advisor: Klaus Leeb), Friedrich-Alexander-Universitaet Erlangen-Nuernberg, 2007.
%H A132431 Reinhard Zumkeller, <a href="/A132431/b132431.txt">Table of n, a(n) for n = 1..250</a>
%F A132431 a(n) = n^n - n*(n-1)^(n-1) - (n-1)*n! + n*(n-1).
%F A132431 a(n) = n*(n-1) + Sum_{k=1..n-2} k*Stirling2(n-1,k)*k!*C(n,k).
%F A132431 a(n) = A060226(n) - A062119(n) + A002378(n-1). - _Reinhard Zumkeller_, Aug 27 2012
%t A132431 Join[{0},Table[n^n-n (n-1)^(n-1)-(n-1)n!+n(n-1),{n,2,20}]] (* _Harvey P. Dale_, Jun 07 2018 *)
%o A132431 (Haskell)
%o A132431 a132431 n = a060226 n - a062119 n + a002378 (n - 1)
%o A132431 -- _Reinhard Zumkeller_, Aug 27 2012
%Y A132431 Cf. A000312, A060226.
%K A132431 nice,nonn
%O A132431 1,2
%A A132431 Simon Bogner (sisibogn(AT)stud.informatik.uni-erlangen.de), Nov 20 2007