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L.g.f.: A(x) = log( 1 + Sum_{n>=1} (n-1)!*x^n ) = Sum_{n>=1} a(n)*x^n/n.
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%I #2 Mar 30 2012 18:37:10

%S 1,1,4,17,91,574,4173,34353,316012,3214181,35832567,434643518,

%T 5700340569,80391481045,1213353891124,19516682949217,333307249446083,

%U 6023617863581806,114854054775272053,2304312940318519977

%N L.g.f.: A(x) = log( 1 + Sum_{n>=1} (n-1)!*x^n ) = Sum_{n>=1} a(n)*x^n/n.

%e L.g.f.: A(x) = x + x^2/2 + 4*x^3/3 + 17*x^4/4 + 91*x^5/5 + 574*x^6/6 +...

%e exp(A(x)) = 1 + x + x^2 + 2*x^3 + 6*x^4 + 24*x^5 + 120*x^6 +...

%o (PARI) {a(n)=polcoeff(x*deriv(log(Ser(concat(1,vector(n+1,k,(k-1)!))))),n)}

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jun 11 2008