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A323321 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( (1+x)^n - 21*x*A(x) )^n * 10^n / 11^(n+1).

%I A323321 #6 Jan 10 2019 22:28:44
%S A323321 1,230,202720,301356010,609471837800,1531246512757400,
%T A323321 4554410421462541300,15575127764655971159900,
%U A323321 60061431635374301463364100,257559473604548074955131621000,1215330203862647096788767608162000,6257647362127152791857282855542122000,34917317338173226632480770480063290796000,209923913089512941533199772776123546222790000,1353013627656130991705167318085125179145490486000
%N A323321 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( (1+x)^n - 21*x*A(x) )^n * 10^n / 11^(n+1).
%F A323321 G.f. A(x) satisfies the following identities.
%F A323321 (1) 1 = Sum_{n>=0} ( (1+x)^n - 21*x*A(x) )^n * 10^n / 11^(n+1).
%F A323321 (2) 1 = Sum_{n>=0} (1+x)^(n^2) * 10^n / (11 + 210*x*A(x)*(1+x)^n)^(n+1).
%e A323321 G.f.: A(x) = 1 + 230*x + 202720*x^2 + 301356010*x^3 + 609471837800*x^4 + 1531246512757400*x^5 + 4554410421462541300*x^6 + 15575127764655971159900*x^7 + ...
%e A323321 such that
%e A323321 1 = 1/11 + ((1+x) - 21*x*A(x))*10/11^2 + ((1+x)^2 - 21*x*A(x))^2*10^2/11^3 + ((1+x)^3 - 21*x*A(x))^3*10^3/11^4 + ((1+x)^4 - 21*x*A(x))^4*10^4/11^5 + ...
%e A323321 Also,
%e A323321 1 = 1/(11 + 210*x*A(x)) + (1+x)*10/(11 + 210*x*A(x)*(1+x))^2 + (1+x)^4*10^2/(11 + 210*x*A(x)*(1+x)^2)^3 + (1+x)^9*10^3/(11 + 210*x*A(x)*(1+x)^3)^4 + ...
%o A323321 (PARI) \p120
%o A323321 {A=vector(1); A[1]=1; for(i=1,20, A = concat(A,0);
%o A323321 A[#A] = round( Vec( sum(n=0, 3000, ( (1+x +x*O(x^#A))^n - 21*x*Ser(A) )^n * 10^n/11^(n+1)*1.)/210 ) )[#A+1]); A}
%Y A323321 Cf. A301435, A303288, A323314, A323315, A323316, A323317, A323318, A323319, A323320.
%K A323321 nonn
%O A323321 0,2
%A A323321 _Paul D. Hanna_, Jan 10 2019