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A200315 E.g.f. satisfies: A(x) = exp(x^5*A(x)^5/5!).

%I A200315 #11 Mar 30 2012 18:37:32
%S A200315 1,1,1386,32288256,4527372986136,2373840824586206976,
%T A200315 3532226719132271834449776,12455133709483299692008910094336,
%U A200315 91656142095228409912231665590704016256,1280796898530759870923631204720457656538791936
%N A200315 E.g.f. satisfies: A(x) = exp(x^5*A(x)^5/5!).
%F A200315 a(n) = (5*n+1)^(n-1) * (5*n)! / (n!*(5!)^n).
%F A200315 E.g.f.: (1/x)*Series_Reversion( x*exp(-x^5/5!) ).
%F A200315 Powers of e.g.f.: define a(n,m) by A(x)^m = Sum_{n>=0} a(n,m)*x^(5*n)/(5*n)!
%F A200315 then a(n,m) = m*(5*n+m)^(n-1) * (5*n)!/(n!*(5!)^n).
%e A200315 E.g.f.: A(x) = 1 + x^5/5! + 1386*x^10/10! + 32288256*x^15/15! +...
%e A200315 where log(A(x)) = x^5*A(x)^5/5! and
%e A200315 A(x)^5 = 1 + 5*x^5/5! + 9450*x^10/10! + 252252000*x^15/15! + 38192529375000*x^20/20! +...
%o A200315 (PARI) {a(n)=(5*n)!*polcoeff(1/x*serreverse(x*(exp(-x^5/5!+x*O(x^(5*n))))),5*n)}
%o A200315 (PARI) {a(n)=(5*n+1)^(n-1)*(5*n)!/(n!*(5!)^n)}
%Y A200315 Cf. A034941, A200313, A200314.
%K A200315 nonn
%O A200315 0,3
%A A200315 _Paul D. Hanna_, Nov 15 2011