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%I #4 Mar 30 2012 18:37:37
%S 1,1,3,9,31,111,415,1591,6229,24773,99793,406197,1667803,6898183,
%T 28710933,120146889,505161063,2132805899,9037954725,38424844083,
%U 163843435737,700477124863,3001906536983,12892683275989,55481600408439,239188767723227,1032889415516779
%N G.f. A(x) satisfies: A(x) = x / [Sum_{n>=1} (-1)^(n-1) * A(x)^(n*(n-1)/2) * (1 - A(x)^n)/(1 - A(x))].
%e G.f.: A(x) = x + x^2 + 3*x^3 + 9*x^4 + 31*x^5 + 111*x^6 + 415*x^7 + 1591*x^8 + 6229*x^9 + 24773*x^10 + 99793*x^11 + 406197*x^12 +...
%e such that the g.f. satisfies:
%e x/A(x) = 1 - A(x)*(1-A(x)^2)/(1-A(x)) + A(x)^3*(1-A(x)^3)/(1-A(x)) - A(x)^6*(1-A(x)^4)/(1-A(x)) + A(x)^10*(1-A(x)^5)/(1-A(x)) -+...
%e Let G(x) satisfy: G(A(x)) = x, then:
%e G(x) = x - (x^2 + x^3) + (x^4 + x^5 + x^6) - (x^7 + x^8 + x^9 + x^10) + (x^11 + x^12 + x^13 + x^14 + x^15) +...
%o (PARI) {a(n)=polcoeff(serreverse(x*sum(m=1,n,(-1)^(m-1)*x^(m*(m-1)/2)*(1-x^m)/(1-x)+x*O(x^n))),n)}
%o for(n=1,30,print1(a(n),", "))
%K nonn
%O 1,3
%A _Paul D. Hanna_, Mar 06 2012
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