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 A174845 #40 Aug 10 2018 18:09:33
%S A174845 1,1,8,153,4981,236970,15211158,1250791640,127078235560,
%T A174845 15531504729378,2237017556966100,373533515381767037,
%U A174845 71351421971134445583,15419725101750288678775,3734978285744386546427032,1005908662614385539285407741,299140901286981469075716747245
%N A174845 O.g.f.: Sum_{n>=0} n^(2*n) * x^n / (1 - n^2*x)^n * exp( -n^2*x / (1 - n^2*x) ) / n!.
%H A174845 G. C. Greubel, <a href="/A174845/b174845.txt">Table of n, a(n) for n = 0..268</a>
%F A174845 a(n) = Sum_{k=1..n} C(n-1,k-1) * S2(2*n,k) for n>0 with a(0)=1. - _Paul D. Hanna_, Mar 08 2013
%e A174845 O.g.f.: A(x) = 1 + x + 8*x^2 + 153*x^3 + 4981*x^4 + 236970*x^5 +...
%e A174845 where
%e A174845 A(x) = 1 + x/(1-x)*exp(-x/(1-x)) + 2^4*x^2/(1-2^2*x)^2*exp(-2^2*x/(1-2^2*x))/2! + 3^6*x^3/(1-3^2*x)^3*exp(-3^2*x/(1-3^2*x))/3! + 4^8*x^4/(1-4^2*x)^4*exp(-4^2*x/(1-4^2*x))/4! +...
%e A174845 simplifies to a power series in x with integer coefficients.
%t A174845 Flatten[{1,Table[Sum[Binomial[n-1,k-1] * StirlingS2[2*n,k],{k,1,n}],{n,1,20}]}] (* _Vaclav Kotesovec_, Aug 11 2014 *)
%t A174845 a[ n_] := SeriesCoefficient[ 1 + Sum[(k^2 x)^k / (1 - k^2 x)^k Exp[-k^2 x / (1 - k^2 x)] / k!, {k, n + 1}], {x, 0, n}]; (* _Michael Somos_, Jun 27 2017 *)
%o A174845 (PARI) a(n)=polcoeff(sum(k=0, n+1, (k^2*x)^k/(1-k^2*x)^k*exp(-k^2*x/(1-k^2*x+x*O(x^n)))/k!), n) \\ _Paul D. Hanna_, Nov 04 2012
%o A174845 for(n=0, 25, print1(a(n), ", "))
%o A174845 (PARI) Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)
%o A174845 {a(n)=if(n==0, 1, sum(k=1, n, binomial(n-1, k-1) * Stirling2(2*n, k)))}
%o A174845 for(n=0,25,print1(a(n),", "))\\ _Paul D. Hanna_, Mar 08 2013
%Y A174845 Cf. A134055, A222053, A222054, A243942, A008277.
%K A174845 nonn
%O A174845 0,3
%A A174845 _Paul D. Hanna_, Nov 06 2012