A195895 E.g.f. satisfies: A(x) = exp(-1) * Sum_{n>=0} exp(x*A(x)^n)/n!.

1, 1, 3, 19, 201, 2996, 57613, 1357987, 37921761, 1224420067, 44884358461, 1841710133330, 83634349451425, 4164470926316377, 225629247763909837, 13214729079087267931, 831997985912417838017, 56038514134260089791916, 4020820086886704204188797

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..100

Formula

E.g.f. satisfies: A(x) = Sum_{n>=0} exp(A(x)^n - 1)*x^n/n!. [From Paul D. Hanna, Sep 27 2011]

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 201*x^4/4! + 2996*x^5/5! +...
where
A(x) = exp(-1)*(exp(x) + exp(x*A(x)) + exp(x*A(x)^2)/2! + exp(x*A(x)^3)/3! +...).

Prog

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

Crossrefs

Cf. A195947.

Sequence in context: A303927 A377740 A288693 * A127502 A175176 A362968

Adjacent sequences: A195892 A195893 A195894 * A195896 A195897 A195898

Keyword

nonn

Author

Paul D. Hanna, Sep 24 2011

Status

approved