cp's OEIS Frontend

A206100 G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1-x^k)^k.

%I A206100 #8 Jan 23 2013 10:35:02
%S A206100 1,1,2,3,6,9,18,27,50,79,135,215,361,564,923,1450,2305,3590,5645,8693,
%T A206100 13479,20611,31560,47880,72601,109195,164126,245109,365282,541642,
%U A206100 801380,1180281,1734332,2538490,3706287,5392883,7827571,11325879,16348515,23530961
%N A206100 G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1-x^k)^k.
%F A206100 G.f.: 1 + x*(1 - G(0))/(1-x) where G(k) =  1 - 1/(1-x^(k+1))^(k+1)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Jan 23 2013
%e A206100 G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 9*x^5 + 18*x^6 + 27*x^7 +...
%e A206100 where
%e A206100 A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-x^2)^2) + x^3/((1-x)*(1-x^2)^2*(1-x^3)^3) + x^4/((1-x)*(1-x^2)^2*(1-x^3)^3*(1-x^4)^4) +...
%o A206100 (PARI) {a(n)=polcoeff(sum(m=0,n,x^m/prod(k=1,m,(1-x^k +x*O(x^n))^k)),n)}
%K A206100 nonn
%O A206100 0,3
%A A206100 _Paul D. Hanna_, Feb 03 2012