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%I A213112 #5 Jun 06 2012 01:05:01
%S A213112 1,1,7,118,2953,109156,5220649,316358470,23113133089,1989812691208,
%T A213112 196917302640241,22027382030604226,2745173167377165793,
%U A213112 376884883299800082988,56471832695739964146505,9164249250078891945300886,1600258838038369930772797249
%N A213112 E.g.f.: A(x) = exp( x/A(-x*A(x)^7)^3 ).
%C A213112 Compare the e.g.f. to:
%C A213112 (1) W(x) = exp(x/W(-x*W(x)^2)^1) when W(x) = Sum_{n>=0} (1*n+1)^(n-1)*x^n/n!.
%C A213112 (2) W(x) = exp(x/W(-x*W(x)^4)^2) when W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!.
%C A213112 (3) W(x) = exp(x/W(-x*W(x)^6)^3) when W(x) = Sum_{n>=0} (3*n+1)^(n-1)*x^n/n!.
%e A213112 E.g.f.: A(x) = 1 + x + 7*x^2/2! + 118*x^3/3! + 2953*x^4/4! + 109156*x^5/5! +...
%e A213112 Related expansions:
%e A213112 A(x)^3 = 1 + 3*x + 27*x^2/2! + 486*x^3/3! + 12825*x^4/4! + 477108*x^5/5! +...
%e A213112 A(x)^7 = 1 + 7*x + 91*x^2/2! + 1918*x^3/3! + 56329*x^4/4! + 2194612*x^5/5! +...
%e A213112 1/A(-x*A(x)^7)^3 = 1 + 3*x + 33*x^2/2! + 603*x^3/3! + 17913*x^4/4! +...
%e A213112 The logarithm of the e.g.f., log(A(x)) = x/A(-x*A(x)^7)^3, begins:
%e A213112 log(A(x)) = x + 6*x^2/2! + 99*x^3/3! + 2412*x^4/4! + 89565*x^5/5! +...
%o A213112 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(x/subst(A^3,x,-x*A^7+x*O(x^n))));n!*polcoeff(A,n)}
%o A213112 for(n=0,25,print1(a(n),", "))
%Y A213112 Cf. A213108, A213109, A213110, A213111, A213113.
%K A213112 nonn
%O A213112 0,3
%A A213112 _Paul D. Hanna_, Jun 05 2012

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