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 A196125 E.g.f. satisfies: A(x) = Sum_{n>=0} exp(x*A(x)^(2*n) - 1)/n!. 0

%I #5 Mar 30 2012 18:37:29

%S 1,1,5,61,1241,35321,1293565,57977333,3074915569,188387127793,

%T 13093624617781,1018008272854189,87546809210311753,

%U 8251472362124225001,845856237057331033773,93695948684292621079141,11153023640354668717741793,1419786005695986152133964769

%N E.g.f. satisfies: A(x) = Sum_{n>=0} exp(x*A(x)^(2*n) - 1)/n!.

%F E.g.f. satisfies: A(x) = Sum_{n>=0} exp(A(x)^(2*n) - 1)*x^n/n!.

%e E.g.f.: A(x) = 1 + x + 5*x^2/2! + 61*x^3/3! + 1241*x^4/4! + 35321*x^5/5! +...

%e where

%e A(x) = exp(x-1) + exp(x*A(x)^2-1) + exp(x*A(x)^4-1)/2! + exp(x*A(x)^6-1)/3! +...

%e Also,

%e A(x) = 1 + exp(A(x)^2-1)*x + exp(A(x)^4-1)*x^2/2! + exp(A(x)^6-1)*x^3/3! +...

%o (PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); for(i=1, n, A=1+sum(m=1, n, exp(A^(2*m)-1)*X^m/m!)); n!*polcoeff(A, n)}

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, 2*n+10, exp(x*A^(2*m)-1+x*O(x^n))/m!)); round(n!*polcoeff(A, n))}

%Y Cf. A195895.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 27 2011

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Last modified November 30 12:38 EST 2023. Contains 367461 sequences. (Running on oeis4.)