A187820 G.f. satisfies: A(x) = x + x*Sum{n>=0} x^n/n! * d^n/dx^n A(x)^(n+1).

1, 1, 3, 12, 62, 377, 2585, 19497, 159113, 1389122, 12868421, 125721997, 1289307566, 13827494435, 154617546534, 1798091282057, 21700908011943, 271305769072192, 3507957527328398, 46842455163101344, 645137348798871851, 9153330597244491848, 133643964236921732563

Offset: 1

Author

Paul D. Hanna, Dec 27 2012

Keywords

• nonn

Comments

Compare to g.f. G(x) = x + x*G(G(x)) of A030266, where:

G(x) = x + x*Sum{n>=0} x^n/n! * d^n/dx^n G(x)^(n+1)/(n+1).

Examples

			G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 62*x^5 + 377*x^6 + 2585*x^7 +...
where
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! +...
		

Crossrefs

Cf. A030266.

Programs

PARI

{Dx(n,F)=local(D=F);for(i=1,n,D=deriv(D));D}
{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)}
for(n=1, 30, print1(a(n), ", "))