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 A045531 #76 Aug 09 2024 01:56:03
%S A045531 1,3,19,175,2101,31031,543607,11012415,253202761,6513215599,
%T A045531 185311670611,5777672071535,195881901213181,7174630439858727,
%U A045531 282325794823047151,11878335717996660991,532092356706983938321,25283323623228812584415,1270184310304975912766347
%N A045531 Number of sticky functions: endofunctions of [n] having a fixed point.
%C A045531 a(n) is also the number of functions f{1,2,...,n}->{1,2,...,n} with at least one element mapped to 1. - _Geoffrey Critzer_, Dec 10 2012
%C A045531 Equivalently, a(n) is the number of endofunctions with minimum 1. - _Olivier Gérard_, Aug 02 2016
%C A045531 Number of bargraphs of width n and height n. Equivalently: number of ordered n-tuples of positive integers such that the largest is n. Example: a(3) = 19 because we have 113, 123, 213, 223, 131, 132, 231, 232, 311, 312, 321, 322, 331, 332, 313, 323, 133, 233, and 333. - _Emeric Deutsch_, Jan 30 2017
%H A045531 Vincenzo Librandi, <a href="/A045531/b045531.txt">Table of n, a(n) for n = 1..100</a>
%H A045531 A. Blecher, C. Brennan, A. Knopfmacher and H. Prodinger, <a href="http://dx.doi.org/10.1016/j.dam.2014.08.026">The height and width of bargraphs</a>, Discrete Applied Math. 180, (2015), 36-44.
%F A045531 a(n) = n^n - (n-1)^n.
%F A045531 E.g.f.: (T - x)/(T-T^2), where T=T(x) is Euler's tree function (see A000169).
%F A045531 With interpolated zeros, ceiling(n/2)^ceiling(n/2) - floor(n/2)^ceiling(n/2). - _Paul Barry_, Jul 13 2005
%F A045531 a(n) = A047969(n,n). - _Alford Arnold_, May 07 2005
%F A045531 a(n) = Sum_{i=1..n} binomial(n,i)*(i-1)^(i-1)*(n-i)^(n-i) = Sum_{i=1..n} binomial(n,i)*A000312(i-1)*A000312(n-i). - _Vladimir Shevelev_, Sep 30 2010
%F A045531 a(n) = Sum_{k=1..n} k!*binomial(n-1,k-1)*Stirling2(n,k). - _Vladimir Kruchinin_, Mar 01 2014
%F A045531 a(n) = A350454(n+1, 1) / (n+1). - _Mélika Tebni_, Dec 20 2022
%F A045531 Limit_{n->oo} a(n)/n^n = 1 - 1/e = A068996. - _Luc Rousseau_, Jan 20 2023
%t A045531 Table[Sum[Binomial[n, i] (n - 1)^(n - i), {i, 1, n}], {n, 1, 20}]
%o A045531 (Magma) [n^n-(n-1)^n: n in [1..20] ]; // _Vincenzo Librandi_, May 07 2011
%o A045531 (PARI) a(n)=n^n-(n-1)^n; \\ _Charles R Greathouse IV_, May 08 2011
%o A045531 (Maxima) a(n) = sum(k!*binomial(n-1,k-1)*stirling2(n,k),k,1,n); /* _Vladimir Kruchinin_, Mar 01 2014 */
%Y A045531 Column |a(n, 2)| of A039621. Row sums of triangle A055858.
%Y A045531 Cf. A000312, A066274, A066275, A047969.
%Y A045531 Column k=1 of A246049.
%Y A045531 Cf. A068996, A350454.
%K A045531 easy,nonn
%O A045531 1,2
%A A045531 _Len Smiley_