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%I #2 Mar 30 2012 18:37:18
%S 1,1,2,4,14,89,1050,28983,2066217,272159513,56735786726,
%T 23441305184736,26635730598676118,64099902414443754551,
%U 241666593661232949435382,1531373212165249576810266758,24642808245610936988728333582900
%N G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^n * x^k] * x^n/n ), an integer series in x.
%F G.f.: exp( Sum_{n>=1} A166895(n)*x^n/n ) where A166895(n) = Sum_{k=0..[n/2]} C(n-k,k)^(n-k)*n/(n-k).
%e G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 14*x^4 + 89*x^5 + 1050*x^6 +...
%e log(A(x)) = x + 3*x^2/2 + 7*x^3/3 + 39*x^4/4 + 366*x^5/5 + 5697*x^6/6 +...+ A166895(n)*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^m*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)^(m-k)*m/(m-k))*x^m/m)+x*O(x^n)), n)}
%Y Cf. A166895.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 23 2009
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