A179324 - OEIS

%I #2 Mar 30 2012 18:37:22

%S 1,5,25,157,1061,7883,61727,508949,4377904,39144035,362532974,

%T 3469415119,34239639968,347923109287,3635414562245,39018272951829,

%U 429753842563060,4853492527491008,56163703072054240,665483565486515787

%N L.g.f.: G(x) = x*exp( Sum_{n>=1} G(G(x^n))/n ) where G(x) = x*exp(Sum_{n>=1} a(n)*x^n/n).

%e G.f.: L(x) = x + 5*x^2/2 + 25*x^3/3 + 157*x^4/4 + 1061*x^5/5 +...

%e G(x) = x*exp(L(x)) = x + x^2 + 3*x^3 + 11*x^4 + 52*x^5 + 280*x^6 + 1705*x^7 + 11275*x^8 + 80120*x^9 + 604111*x^10 +...+ A179322(n)*x^n +...

%e L(x) = log(G(x)/x) = G(G(x)) + G(G(x^2))/2 + G(G(x^3))/3 + G(G(x^4))/4 + G(G(x^5))/5 + G(G(x^6))/6 +...+ G(G(x^n))/n +...

%o (PARI) {a(n)=local(A=x);for(i=1,n,A=x*exp(sum(m=1,n,subst(A,x,(subst(A,x,x^m+x*O(x^n))))/m)));n*polcoeff(log(A/x),n)}

%Y Cf. A179322, A179323.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jul 16 2010