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 A245496 #23 Jul 19 2022 11:53:01
%S A245496 1,2,10,87,1096,18045,365796,8793337,244327616,7701562377,
%T A245496 271493172100,10582453248741,451909972458000,20980984760560045,
%U A245496 1052197311966267572,56683993296812515425,3264626390205804733696,200168726219982496336401,13017989155680578824221060
%N A245496 a(n) = n! * [x^n] (exp(x)+x)^n.
%C A245496 a(n) is the number of ways to place n labeled balls (colored red and blue) into n labeled bins so that if a blue ball occupies a bin then there are no other balls with it. - _Geoffrey Critzer_, Jan 30 2015
%H A245496 Vincenzo Librandi, <a href="/A245496/b245496.txt">Table of n, a(n) for n = 0..200</a>
%F A245496 a(n) ~ (1+exp(-1))^(n+1/2) * n^n.
%F A245496 E.g.f.: 1 / ((1 - x) * (1 + LambertW(-x/(1 - x)))). - _Ilya Gutkovskiy_, Jan 25 2020
%F A245496 a(n) = n! * Sum_{k=0..n} k^k/k! * binomial(n,k). - _Seiichi Manyama_, Jul 19 2022
%t A245496 Table[n!*SeriesCoefficient[(E^x+x)^n, {x, 0, n}], {n, 0, 20}]
%t A245496 Flatten[{1,Table[n!+Sum[Binomial[n,j]^2*(n-j)^(n-j)*j!,{j,0,n-1}],{n,1,20}]}]
%o A245496 (PARI) seq(n)={Vec(serlaplace(1/((1 - x) * (1 + lambertw(-x/(1 - x) + O(x*x^n))))), -(n+1))} \\ _Andrew Howroyd_, Jan 25 2020
%o A245496 (PARI) a(n) = n!*sum(k=0, n, k^k/k!*binomial(n, k)); \\ _Seiichi Manyama_, Jul 19 2022
%Y A245496 Cf. A231797, A245493, A245405, A331726.
%K A245496 nonn,easy
%O A245496 0,2
%A A245496 _Vaclav Kotesovec_, Jul 24 2014