Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Apr 16 2021 15:46:44
%S 1,1,1,3,5,11,27,55,127,285,647,1457,3297,7489,16945,38523,87293,
%T 198179,449907,1021135,2318527,5263581,11950967,27133985,61609953,
%U 139888777,317629465,721215027,1637598485,3718378619,8443065363,19171129327
%N G.f. = continued fraction: A(x)=1/(1-x/(1-2*x^2/(1-3*x^3/(1-4*x^4/(...))))).
%H Seiichi Manyama, <a href="/A088357/b088357.txt">Table of n, a(n) for n = 0..100</a>
%F G.f.: T(0), where T(k) = 1 - x^(k+1)*(k+1)/( x^(k+1)*(k+1) - 1/T(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Oct 26 2013
%F a(n) ~ c * d^n, where d = 2.2706470084004562621321821916243432273516... and c = 0.1745837410025587240288929391139119506... - _Vaclav Kotesovec_, Aug 25 2017
%t nmax = 50; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[Range[nmax + 1]*x^Range[nmax + 1]]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 25 2017 *)
%o (PARI) S=1; L=30; for(k=1,L,m=L-k+1; S=1/(1-m*x^m*S)+x*O(x^L)); A(x)=S; a(n)=polcoeff(A(x),n,x)
%Y Cf. A005169, A285381.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Sep 26 2003