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E.g.f. A(x) satisfies: Sum_{n>=0} 3^(n^2-n) * x^n/n! / A(3^n*x) = 1.
1

%I #3 Oct 27 2012 23:38:38

%S 1,1,5,429,399273,3072726201,195746363156205,107315772169710355749,

%T 519518439242514267271247313,22466597296811866577087885119239921,

%U 8719095388372045822565716229498060925301845,30421189091577923093547933001708849981738642279605789

%N E.g.f. A(x) satisfies: Sum_{n>=0} 3^(n^2-n) * x^n/n! / A(3^n*x) = 1.

%e E.g.f.: A(x) = 1 + x + 5*x^2/2! + 429*x^3/3! + 399273*x^4/4! + 3072726201*x^5/5! +...

%e where

%e 1 = 1/A(x) + x/A(3*x) + 3^2*x^2/2!/A(3^2*x) + 3^6*x^3/3!/A(3^3*x) + 3^12*x^4/4!/A(3^4*x) + 3^20*x^5/5!/A(3^5*x) + 3^30*x^6/6!/A(3^6*x) +....

%o (PARI) {a(n)=local(A=1+sum(k=1,n-1,a(k)*x^k/k!)+x*O(x^n));n!*polcoeff(sum(k=0,n,3^(k^2-k)*x^k/k!/subst(A,x,3^k*x)),n)}

%o for(n=0,15,print1(a(n),", "))

%Y Cf. A054948.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 27 2012