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%I #2 Mar 30 2012 18:37:16
%S 1,3,9,99,1917,324567,65546253,121237985007,231991261827633,
%T 4053251131970038227,71801958531451566872745,
%U 11561440390042361895766055043,1877401313066393527954697682635421
%N G.f.: A(x) = exp( Sum_{n>=1} 3^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.
%F a(n) = (1/n)*Sum_{k=1..n} 3^floor((k^2+1)/2) * a(n-k) for n>0, with a(0)=1.
%e G.f.: A(x) = 1 + 3*x + 9*x^2 + 99*x^3 + 1917*x^4 + 324567*x^5 +...
%e log(A(x)) = 3*x + 3^2*x^2/2 + 3^5*x^3/3 + 3^8*x^4/4 + 3^13*x^5/5 + 3^18*x^6/6 +...
%o (PARI) {a(n)=polcoeff(exp(sum(k=1, n, 3^floor((k^2+1)/2)*x^k/k)+x*O(x^n)), n)}
%Y Cf. A156335, A156337, A155203.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Feb 10 2009