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%I #5 Apr 20 2019 09:59:46
%S 1,13,2169,2978509,9280313659,48235745422023,369813382363308535,
%T 3909740189577825437323,54527701144836157579584201,
%U 970962668611869711040922366005,21515265687657935356949478953957425,580980133435728709625260571749908867477,18788362634592779032654472355826818388313283,717059741765903711219719995640847718723285774351
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} (1 + 3*x)^(n^3) / A(x)^(n^2) * 1/2^(n+1).
%H Paul D. Hanna, <a href="/A325216/b325216.txt">Table of n, a(n) for n = 0..50</a>
%e G.f.: A(x) =1 + 13*x + 2169*x^2 + 2978509*x^3 + 9280313659*x^4 + 48235745422023*x^5 + 369813382363308535*x^6 + 3909740189577825437323*x^7 + ...
%e such that
%e 1 = 1/2 + (1+3*x)/A(x)*1/2^2 + (1+3*x)^8/A(x)^4*1/2^3 + (1+3*x)^27/A(x)^9*1/2^4 + (1+3*x)^64/A(x)^16*1/2^5 + (1+3*x)^125/A(x)^25*1/2^6 + (1+3*x)^216/A(x)^36*1/2^7 + (1+3*x)^343/A(x)^49*1/2^8 + (1+3*x)^512/A(x)^64*1/2^9 + ...
%o (PARI) /* Requires suitable precision */
%o {a(n) = my(A=[1]); for(i=0,n,
%o A=concat(A,0); A[#A] = round( polcoeff( sum(n=0,30*#A+100,(1 + 3*x +x*O(x^#A))^(n^3) / Ser(A)^(n^2) * 1/2^(n+1)*1.),#A-1))/3;);A[n+1]}
%o for(n=0,20,print1(a(n),", "))
%K nonn
%O 0,2
%A _Paul D. Hanna_, Apr 19 2019
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