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A187820 G.f. satisfies: A(x) = x + x*Sum{n>=0} x^n/n! * d^n/dx^n A(x)^(n+1). 0
1, 1, 3, 12, 62, 377, 2585, 19497, 159113, 1389122, 12868421, 125721997, 1289307566, 13827494435, 154617546534, 1798091282057, 21700908011943, 271305769072192, 3507957527328398, 46842455163101344, 645137348798871851, 9153330597244491848, 133643964236921732563 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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).

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

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! +...

PROG

(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), ", "))

CROSSREFS

Cf. A030266.

Sequence in context: A258798 A074516 A045740 * A074529 A143916 A323630

Adjacent sequences:  A187817 A187818 A187819 * A187821 A187822 A187823

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 27 2012

STATUS

approved

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Last modified September 20 08:10 EDT 2021. Contains 347577 sequences. (Running on oeis4.)