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

1, 1, 5, 61, 1241, 35321, 1293565, 57977333, 3074915569, 188387127793, 13093624617781, 1018008272854189, 87546809210311753, 8251472362124225001, 845856237057331033773, 93695948684292621079141, 11153023640354668717741793, 1419786005695986152133964769

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

Example

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

Prog

 (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)}
(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))}

Crossrefs

Cf. A195895.

Sequence in context: A371371 A009825 A065919 * A345103 A367385 A096537

Adjacent sequences: A196122 A196123 A196124 * A196126 A196127 A196128

Keyword

nonn

Author

Paul D. Hanna, Sep 27 2011

Status

approved