A195895 - OEIS

%I #9 Mar 30 2012 18:37:29

%S 1,1,3,19,201,2996,57613,1357987,37921761,1224420067,44884358461,

%T 1841710133330,83634349451425,4164470926316377,225629247763909837,

%U 13214729079087267931,831997985912417838017,56038514134260089791916,4020820086886704204188797

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

%H Paul D. Hanna, <a href="/A195895/b195895.txt">Table of n, a(n) for n = 0..100</a>

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

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

%e where

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

%o (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))}

%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^m-1)*X^m/m!)); n!*polcoeff(A, n)}

%Y  Cf. A195947.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 24 2011