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G.f.: exp( Sum_{n>=1} A168591(n)*x^n/n ), where A168591(n) = sum of the n-th power of the trinomial coefficients in row n of triangle A027907.
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%I #2 Mar 30 2012 18:37:20

%S 1,3,14,310,71399,153056789,2826352872319,445742192193898313,

%T 602479884829000885595175,7000510736697461064666950774905,

%U 701725717683874683612335083605682943282

%N G.f.: exp( Sum_{n>=1} A168591(n)*x^n/n ), where A168591(n) = sum of the n-th power of the trinomial coefficients in row n of triangle A027907.

%e G.f.: A(x) = 1 + 3*x + 14*x^2 + 310*x^3 + 71399*x^4 +...

%e log(A(x)) = 3*x + 19*x^2/2 + 831*x^3/3 + 281907*x^4/4 +...+ A168591(n)*x^n/n +...

%o (PARI) {a(n)=if(n==0,1,polcoeff(exp(sum(m=1,n,sum(k=0,2*m,polcoeff((1+x+x^2)^m,k)^m)*x^m/m) +x*O(x^n)),n))}

%Y Cf. A168591, A168592, A168593, A027907.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 01 2009