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A211826 G.f. satisfies: A(x) = 1 + x*( d/dx x*A(x) )^5.

%I A211826 #6 Aug 24 2017 08:39:30
%S A211826 1,1,10,190,5080,170080,6724432,303476320,15300084160,849174449680,
%T A211826 51341667458240,3354970165353120,235493617889171200,
%U A211826 17667618435092524160,1410845692308772162560,119491232651437498097920,10700209630623386429434880,1010278582501924072528588800
%N A211826 G.f. satisfies: A(x) = 1 + x*( d/dx x*A(x) )^5.
%H A211826 Vaclav Kotesovec, <a href="/A211826/b211826.txt">Table of n, a(n) for n = 0..250</a>
%F A211826 G.f. satisfies: A(x) = 1 + x*(A(x) + x*A'(x))^5.
%F A211826 a(n) ~ c * 5^n * n^(8/5) * n!, where c = 0.04375376183367762... - _Vaclav Kotesovec_, Aug 24 2017
%e A211826 G.f.: A(x) = 1 + x + 10*x^2 + 190*x^3 + 5080*x^4 + 170080*x^5 +...
%e A211826 Related expansions:
%e A211826 d/dx x*A(x) = 1 + 2*x + 30*x^2 + 760*x^3 + 25400*x^4 + 1020480*x^5 +...
%e A211826 A'(x) = 1 + 20*x + 570*x^2 + 20320*x^3 + 850400*x^4 + 40346592*x^5 +...
%o A211826 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x*deriv(x*A)^5);polcoeff(A,n)}
%o A211826 for(n=0,25,print1(a(n),", "))
%Y A211826 Cf. A112915, A211824, A211825.
%K A211826 nonn
%O A211826 0,3
%A A211826 _Paul D. Hanna_, Apr 21 2012