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 A112242 #29 Sep 07 2024 01:08:05
%S A112242 1,1,5,25,169,1361,12781,136585,1633745,21594529,312239701,4898379641,
%T A112242 82810239865,1500015354865,28970936174909,594083320767721,
%U A112242 12886811207794081,294742414455540545,7087332775240107685,178707496551303048409,4714241296084031285321,129830157857411005318801
%N A112242 E.g.f. exp( x*(1+x)/(1-x) ).
%C A112242 In general, e.g.f. exp(x*(1+a*x)/(1-b*x)) has general term sum{i=0..n, sum{j=0..n, a^j*b^(n-i-j)*C(i,j)*C(n-j-1,n-i-j)*n!/i!}}.
%H A112242 Seiichi Manyama, <a href="/A112242/b112242.txt">Table of n, a(n) for n = 0..441</a>
%F A112242 E.g.f.: exp(x*(1+x)/(1-x)).
%F A112242 a(n) = Sum_{i=0..n} Sum_{j=0..n} C(i, j)*C(n-j-1, n-i-j)*n!/i!.
%F A112242 D-finite with recurrence: a(n) = (2*n-1)*a(n-1) - (n-4)*(n-1)*a(n-2) - (n-2)*(n-1)*a(n-3). - _Vaclav Kotesovec_, Jun 27 2013
%F A112242 a(n) ~ 2^(-1/4)*exp(2*sqrt(2*n)-2-n)*n^(n-1/4). - _Vaclav Kotesovec_, Jun 27 2013
%t A112242 Range[0, 18]!*CoefficientList[ Series[ Exp[x(1+x)/(1-x)], {x, 0, 18}], x] (* _Zerinvary Lajos_, Mar 23 2007 *)
%o A112242 (PARI)
%o A112242 x='x+O('x^33);
%o A112242 Vec(serlaplace(exp( x*(1+x)/(1-x) )))
%o A112242 /* _Joerg Arndt_, Sep 14 2012 */
%K A112242 easy,nonn
%O A112242 0,3
%A A112242 _Paul Barry_, Aug 29 2005