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%I #2 Mar 30 2012 18:37:18
%S 1,1,2,6,16,45,142,459,1508,5122,17787,62649,223971,811339,2970032,
%T 10974150,40893393,153512844,580082454,2205046961,8427087958,
%U 32362949488,124837337235,483508287359,1879669861074,7332469937755
%N G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k] * x^n/n ), an integer series in x.
%F G.f.: exp( Sum_{n>=1} A166897(n)*x^n/n ) where A166897(n) = Sum_{k=0..[n/2]} C(n-k,k)^3*n/(n-k).
%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 16*x^4 + 45*x^5 + 142*x^6 + 459*x^7 +...
%e log(A(x)) = x + 3*x^2/2 + 13*x^3/3 + 39*x^4/4 + 126*x^5/5 + 477*x^6/6 + 1765*x^7/7 +...+ A166897(n)*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^3*x^k)*x^m/m)+x*O(x^n)), n)}
%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m\2, binomial(m-k, k)^3*m/(m-k))*x^m/m)+x*O(x^n)), n)}
%Y Cf. A166897, variants: A166894, A166898.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 23 2009
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