%I #21 Nov 02 2014 12:55:01
%S 1,1,3,9,33,137,635,3233,17881,106489,678091,4590225,32873625,
%T 248056497,1965232403,16297012121,141080069057,1271902272241,
%U 11916559511731,115805756278393,1165319447579313,12123219789825273,130206136096941195
%N G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (1+k*x)/(1-k*x).
%H Vaclav Kotesovec, <a href="/A193110/b193110.txt">Table of n, a(n) for n = 0..370</a>
%F G.f.: 1 + x*(1 - G(0) )/(1-x) where G(k) = 1 - (1+x*(k+1))/(1-x*(k+1))/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Jan 18 2013
%e G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 33*x^4 + 137*x^5 + 635*x^6 +...
%e where
%e A(x) = 1 + x*(1+x)/(1-x) + x^2*(1+x)*(1+2*x)/((1-x)*(1-2*x)) + x^3*(1+x)*(1+2*x)*(1+3*x)/((1-x)*(1-2*x)*(1-3*x)) +...
%o (PARI) {a(n)=polcoeff(sum(m=0,n,x^m*prod(k=1,m,1+k*x)/prod(k=1,m,1-k*x +x*O(x^n))),n)}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 21 2011