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%I #7 Jan 01 2025 14:40:03
%S 1,8,532,62624,10964914,2399234384,609215149096,171739556144192,
%T 52316948995446679,16918106849112020088,5736533516906891508780,
%U 2021549577502367744673888,735516733692051220039803750,274907827442478316252748869104,105138174536582510069969443280760
%N G.f.: A(x) = exp( Sum_{n>=1} A000172(n)^3*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
%e G.f.: A(x) = 1 + 8*x + 532*x^2 + 62624*x^3 + 10964914*x^4 + 2399234384*x^5 +...
%e where
%e log(A(x)) = 2^3*x + 10^3*x^2/2 + 56^3*x^3/3 + 346^3*x^4/4 + 2252^3*x^5/5 + 15184^3*x^6/6 + 104960^3*x^7/7 +...+ A000172(n)^3*x^n/n +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^3)^3*x^m*1^m/m+x*O(x^n)))); polcoeff(A, n)}
%o for(n=0, 31, print1(a(n), ", "))
%Y Cf. A166990, A216352, A216354, A216355, A052144, A000172.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Sep 04 2012