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 A227207 #15 Jan 31 2022 10:15:31
%S A227207 1,1,6,105,3568,204745,18028266,2278860535,394667414016,
%T A227207 90302033890953,26525942216131330,9775058594870836861,
%U A227207 4433256936788979640848,2434899483389881601250937,1597444746833206096334387802,1237091666097626095124512681755,1119205949224015886848972396596736
%N A227207 E.g.f.: Sum_{n>=0} n^n * x^n / (n! * Product_{k=0..n} (1 - n*k*x)).
%H A227207 Seiichi Manyama, <a href="/A227207/b227207.txt">Table of n, a(n) for n = 0..212</a>
%F A227207 Sum_{n>=0} a(n)*x^n / n!^2 = Sum_{n>=0} (exp(n*x) - 1)^n / n!^2.
%F A227207 a(n) = n! * Sum_{k=0..n} k^n * Stirling2(n,k) / k!.
%e A227207 E.g.f.: A(x) = 1 + x + 6*x^2/2! + 105*x^3/3! + 3568*x^4/4! + 204745*x^5/5! +...
%e A227207 where
%e A227207 A(x) = 1 + x/(1-x) + 2^2*x^2/(2!*(1-2*1*x)*(1-2*2*x)) + 3^3*x^3/(3!*(1-3*1*x)*(1-3*2*x)*(1-3*3*x)) + 4^4*x^4/(4!*(1-4*1*x)*(1-4*2*x)*(1-4*3*x)*(1-4*4*x)) +...
%t A227207 Flatten[{1,Table[n! * Sum[k^n * StirlingS2[n,k] / k!,{k,0,n}],{n,1,20}]}] (* _Vaclav Kotesovec_, May 08 2014 *)
%o A227207 (PARI) {a(n)=n!*polcoeff(sum(m=0, 20, m^m*x^m/m!/prod(k=1, m, 1-m*k*x +x*O(x^n))), n)}
%o A227207 for(n=0, 20, print1(a(n), ", "))
%o A227207 (PARI) {a(n)=n!^2*polcoeff(sum(m=0, n, (exp(m*x+x*O(x^n))-1)^m/m!^2), n)}
%o A227207 for(n=0, 20, print1(a(n), ", "))
%o A227207 (PARI) {a(n)=n!*sum(k=0, n, k^n*stirling(n, k, 2)/k!)}
%o A227207 for(n=0, 20, print1(a(n), ", "))
%Y A227207 Cf. A119392, A229257, A229258, A229259, A229260, A229261.
%Y A227207 Cf. A229233, A229234, A220181, A122399.
%K A227207 nonn
%O A227207 0,3
%A A227207 _Paul D. Hanna_, Sep 18 2013