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 A206100 G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1-x^k)^k. 5

%I #8 Jan 23 2013 10:35:02

%S 1,1,2,3,6,9,18,27,50,79,135,215,361,564,923,1450,2305,3590,5645,8693,

%T 13479,20611,31560,47880,72601,109195,164126,245109,365282,541642,

%U 801380,1180281,1734332,2538490,3706287,5392883,7827571,11325879,16348515,23530961

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

%F 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 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 where

%e 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 (PARI) {a(n)=polcoeff(sum(m=0,n,x^m/prod(k=1,m,(1-x^k +x*O(x^n))^k)),n)}

%K nonn

%O 0,3

%A _Paul D. Hanna_, Feb 03 2012

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Last modified September 25 12:56 EDT 2023. Contains 365647 sequences. (Running on oeis4.)