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%I #9 Mar 10 2018 10:35:55
%S 1,1,5,55,1025,28638,1117831,58157100,3895841625,327054041995,
%T 33660663702514,4170641243258042,612634528823952155,
%U 105303950053511041900,20943400410601239618360,4772694556432364600596272,1235587041134996933696367753,360653856192923791041427500825,117894515649092645422159124253775,42901062533218086978322192560871705
%N a(n) = A300617(n) / (n*(n+1)/2) for n>=1.
%C It is conjectured that this sequence consists entirely of integers.
%C O.g.f. G(x) of A300617 satisfies: [x^n] exp(n*G(x)) = n^2 * [x^(n-1)] exp(n*G(x)) for n>=1.
%H Paul D. Hanna, <a href="/A300589/b300589.txt">Table of n, a(n) for n = 1..300</a>
%o (PARI) {a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^(#A-1)); A[#A] = ((#A-1)^2*V[#A-1] - V[#A])/(#A-1) ); polcoeff( log(Ser(A)), n) / (n*(n+1)/2)}
%o for(n=1, 20, print1(a(n), ", "))
%Y Cf. A300617, A300616.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Mar 10 2018
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