|
%I #8 Dec 27 2012 01:34:10
%S 1,1,3,12,62,377,2585,19497,159113,1389122,12868421,125721997,
%T 1289307566,13827494435,154617546534,1798091282057,21700908011943,
%U 271305769072192,3507957527328398,46842455163101344,645137348798871851,9153330597244491848,133643964236921732563
%N G.f. satisfies: A(x) = x + x*Sum{n>=0} x^n/n! * d^n/dx^n A(x)^(n+1).
%C Compare to g.f. G(x) = x + x*G(G(x)) of A030266, where:
%C G(x) = x + x*Sum{n>=0} x^n/n! * d^n/dx^n G(x)^(n+1)/(n+1).
%e G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 62*x^5 + 377*x^6 + 2585*x^7 +...
%e where
%e A(x) = x + x*A(x)/0! + x^2*d/dx A(x)^2/1! + x^3*d^2/dx^2 A(x)^3/2! + x^4*d^3/dx^3 A(x)^4/3! + x^5*d^4/dx^4 A(x)^5/4! +...
%o (PARI) {Dx(n,F)=local(D=F);for(i=1,n,D=deriv(D));D}
%o {a(n)=local(A=x+x*O(x^n)); for(i=1,n,A=x+x*sum(m=0,n,x^m/m!*Dx(m,(A+x*O(x^n))^(m+1)) )); polcoeff(A, n)}
%o for(n=1, 30, print1(a(n), ", "))
%Y Cf. A030266.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Dec 27 2012
|
