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%I #8 Jan 01 2025 14:40:07
%S 1,4,58,1256,35771,1200188,45016678,1827941560,78753548245,
%T 3551810922324,166120394053698,8002733850225288,395089619067741926,
%U 19911864121386482264,1021345223473335336668,53190166903606336969840,2807000233813092463820488,149869216802426305919295328
%N G.f.: A(x) = exp( Sum_{n>=1} A000172(n)^2*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
%e G.f.: A(x) = 1 + 4*x + 58*x^2 + 1256*x^3 + 35771*x^4 + 1200188*x^5 +...
%e such that
%e log(A(x)) = 4*x + 100*x^2/2 + 3136*x^3/3 + 119716*x^4/4 + 5071504*x^5/5 +...+ A000172(n)^2*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)^2*x^m*1^m/m+x*O(x^n)))); polcoeff(A, n)}
%o for(n=0, 31, print1(a(n), ", "))
%Y Cf. A166990, A216353, A216354, A216355, A052144, A000172.
%K nonn,changed
%O 0,2
%A _Paul D. Hanna_, Sep 04 2012