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A198520 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x)^n / A(x^n) * x^n/n ). 1

%I

%S 1,1,1,2,4,9,22,55,141,370,986,2662,7264,20006,55534,155219,436456,

%T 1233822,3504482,9996417,28624038,82248498,237082689,685375920,

%U 1986604360,5772399530,16810591254,49059068617,143450142998,420213814655,1233034693847,3623838769503

%N G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x)^n / A(x^n) * x^n/n ).

%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 22*x^6 + 55*x^7 +...

%e where

%e log(A(x)) = x + A(x)^2/A(x^2)*x^2/2 + A(x)^3/A(x^3)*x^3/3 + A(x)^4/A(x^4)*x^4/4 +...

%e more explicitly,

%e log(A(x)) = x + x^2/2 + 4*x^3/3 + 9*x^4/4 + 26*x^5/5 + 76*x^6/6 + 218*x^7/7 +...

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

%Y Cf. A198413.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Oct 26 2011

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Last modified November 21 04:22 EST 2019. Contains 329350 sequences. (Running on oeis4.)