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%I #5 Jan 10 2019 22:12:22
%S 1,65,15685,6376505,3524871325,2420187902975,1967093055766825,
%T 1838251199473028225,1937082794808580188025,2269921874941072916242625,
%U 2926922052137279952439869625,4118264067683762888405147993375,6279611163775388892921689107812625,10316794138820163374949788420225125625,18170957626950430345183391610737313950125,34161178486729901360568404660435153779920125
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} ( (1+x)^n - 11*x*A(x) )^n * 5^n / 6^(n+1).
%F G.f. A(x) satisfies the following identities.
%F (1) 1 = Sum_{n>=0} ( (1+x)^n - 11*x*A(x) )^n * 5^n / 6^(n+1).
%F (2) 1 = Sum_{n>=0} (1+x)^(n^2) * 5^n / (6 + 55*x*A(x)*(1+x)^n)^(n+1).
%e G.f.: A(x) = 1 + 65*x + 15685*x^2 + 6376505*x^3 + 3524871325*x^4 + 2420187902975*x^5 + 1967093055766825*x^6 + 1838251199473028225*x^7 + ...
%e such that
%e 1 = 1/6 + ((1+x) - 11*x*A(x))*5/6^2 + ((1+x)^2 - 11*x*A(x))^2*5^2/6^3 + ((1+x)^3 - 11*x*A(x))^3*5^3/6^4 + ((1+x)^4 - 11*x*A(x))^4*5^4/6^5 + ...
%e Also,
%e 1 = 1/(6 + 55*x*A(x)) + (1+x)*5/(6 + 55*x*A(x)*(1+x))^2 + (1+x)^4*5^2/(6 + 55*x*A(x)*(1+x)^2)^3 + (1+x)^9*5^3/(6 + 55*x*A(x)*(1+x)^3)^4 + ...
%o (PARI) \p120
%o {A=vector(1); A[1]=1; for(i=1,20, A = concat(A,0);
%o A[#A] = round( Vec( sum(n=0,1200, ( (1+x +x*O(x^#A))^n - 11*x*Ser(A) )^n * 5^n/6^(n+1)*1.)/55 ) )[#A+1]); A}
%Y Cf. A301435, A303288, A323314, A323315, A323317, A323318, A323319, A323320, A323321.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 10 2019
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