The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182264 G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n/n! * d^n/dx^n x*A(x)^n. 2

%I

%S 1,1,4,54,1928,164650,32676492,14876772190,15354661251344,

%T 35516102976906066,182198338264587667220,2054287821808180963790214,

%U 50510836264662863485736461464,2690257723573942460914976734069882,308577942946685093647137438456317429148

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

%H Vaclav Kotesovec, <a href="/A182264/b182264.txt">Table of n, a(n) for n = 0..77</a>

%F a(n) ~ c * n! * 2^(n*(n-1)/2), where c = 1.429815286617205023097354008... - _Vaclav Kotesovec_, Feb 22 2014

%e G.f.: A(x) = 1 + x + 4*x^2 + 54*x^3 + 1928*x^4 + 164650*x^5 + 32676492*x^6 +...

%o (PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D} /* n-th derivative of F */

%o {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+sum(k=1, n, x^k/k!*Dx(k, x*A^k+x*O(x^n) ))); polcoeff(A, n)}

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A182263.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Apr 21 2012

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 1 05:25 EDT 2023. Contains 361673 sequences. (Running on oeis4.)