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A168593 G.f.: exp( Sum_{n>=1} A132303(n)*x^n/n ), where A132303(n) = sum of the cubes of the trinomial coefficients in row n of triangle A027907.

%I A168593 #5 Feb 28 2015 22:16:14
%S A168593 1,3,27,349,5484,96408,1824758,36393090,754696998,16130052394,
%T A168593 353134333470,7884110379006,178908263232959,4115917059924057,
%U A168593 95806493175049929,2252809457441037107,53443567449376649304
%N A168593 G.f.: exp( Sum_{n>=1} A132303(n)*x^n/n ), where A132303(n) = sum of the cubes of the trinomial coefficients in row n of triangle A027907.
%C A168593  Self-convolution cube-root yields the integer sequence A251686.
%e A168593 G.f.: A(x) = 1 + 3*x + 27*x^2 + 349*x^3 + 5484*x^4 + 96408*x^5 +...
%e A168593 log(A(x)) = 3*x + 45*x^2/2 + 831*x^3/3 + 17181*x^4/4 + 375903*x^5/5 +...+ A132303(n)*x^n/n +...
%o A168593 (PARI) {A027907(n,k) = polcoeff((1+x+x^2)^n, k)}
%o A168593 {A132303(n) = sum(k=0, 2*n, A027907(n,k)^3)}
%o A168593 {a(n) = local(A); A = exp(sum(m=1, n+1, A132303(m)*x^m/m) +x*O(x^n)); polcoeff(A,n)}
%o A168593 for(n=0,30,print1(a(n),", "))
%Y A168593 Cf. A168590, A168592, A132303, A027907, A251686.
%K A168593 nonn
%O A168593 0,2
%A A168593 _Paul D. Hanna_, Dec 01 2009