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A166898 G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^4 * x^k] * x^n/n ), an integer series in x.

%I A166898 #2 Mar 30 2012 18:37:18
%S A166898 1,1,2,10,38,137,646,3241,15623,79439,427562,2317396,12715372,
%T A166898 71543343,408543758,2353591560,13717994046,80827739181,480016288156,
%U A166898 2871701561720,17304832805996,104933348346951,639814473417775
%N A166898 G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^4 * x^k] * x^n/n ), an integer series in x.
%F A166898 G.f.: exp( Sum_{n>=1} A166899(n)*x^n/n ) where A166899(n) = Sum_{k=0..[n/2]} C(n-k,k)^4*n/(n-k).
%e A166898 G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 38*x^4 + 137*x^5 + 646*x^6 + 3241*x^7 +...
%e A166898 log(A(x)) = x + 3*x^2/2 + 25*x^3/3 + 111*x^4/4 + 456*x^5/5 + 2697*x^6/6 + 15961*x^7/7 +...+ A166899(n)*x^n/n +...
%o A166898 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^4*x^k)*x^m/m)+x*O(x^n)), n)}
%o A166898 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m\2, binomial(m-k, k)^4*m/(m-k))*x^m/m)+x*O(x^n)), n)}
%Y A166898 Cf. A166897, variants: A166894, A166898.
%K A166898 nonn
%O A166898 0,3
%A A166898 _Paul D. Hanna_, Nov 23 2009