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 A193668 #20 Sep 26 2015 13:56:59
%S A193668 1,1,5,24,134,866,6392,53198,493628,5057522,56741240,692118422,
%T A193668 9122245508,129220379978,1958059133552,31607140330670,541515698082332,
%U A193668 9814691158604258,187629572002767848,3773371262361852422,79636835475910932020
%N A193668 a(n) = Sum_{i=0..n-1} (n+i)*a(n-1-i) for n>1, a(0)=1, a(1)=1.
%C A193668 Occurs in making the Q-residue A193657.
%C A193668 Second difference of A002627. - _Peter Luschny_, May 30 2014
%H A193668 Vincenzo Librandi, <a href="/A193668/b193668.txt">Table of n, a(n) for n = 0..200</a>
%F A193668 Recurrence: a(n) = (n+2)*a(n-1) - (n-2)*a(n-2). - _Vaclav Kotesovec_, Nov 20 2012
%F A193668 a(n) ~ n!*n*(e-1). - _Vaclav Kotesovec_, Nov 20 2012
%F A193668 a(n) = (n-n^2-1)*Gamma(n) + e*(n*Gamma(n+1,1)-(n-1)*Gamma(n,1)) for n>0. - _Peter Luschny_, May 30 2014.
%p A193668 a := n -> `if`(n=0,1,(n-n^2-1)*GAMMA(n)+exp(1)*((1-n)*GAMMA(n,1) + n*GAMMA(n+1, 1))): seq(simplify(a(n)),n=0..20); # _Peter Luschny_, May 30 2014
%t A193668 (See A193657.)
%t A193668 Flatten[{1,RecurrenceTable[{(n-2)*a[n-2] - (n+2)*a[n-1] + a[n] == 0, a[1]==1, a[2]==5}, a, {n, 20}]}] (* _Vaclav Kotesovec_, Nov 20 2012 *)
%t A193668 CoefficientList[Series[Log[x-1]+E*Gamma[0,1-x]-E*Gamma[0,1]+1-I*Pi+(E^x*x-x^2)/(x-1)^2, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Nov 20 2012 *)
%o A193668 (PARI) a(n)=if(n<2,1,sum(i=0,n-1,(n+i)*a(n-1-i))) \\ _Charles R Greathouse IV_, May 30 2014
%Y A193668 Cf. A193657, A002627.
%K A193668 nonn
%O A193668 0,3
%A A193668 _Clark Kimberling_, Aug 02 2011