A131310 - OEIS

%I #7 Mar 11 2016 17:04:30

%S 1,1,3,25,697,87261,63362851,319794398533,12896670350677905,

%T 4680059818474453354777,16983047870459137946598471811,

%U 677909112049327323648624151866814641

%N O.g.f. A(x) satisfies: [x^n] exp(x*A(x)) = [x^n] A(x) / n!.

%F a(n+1) = n!*Sum_{k=0..n} (k+1)/(n-k)!*a(k)*a(n-k). - _Vladeta Jovovic_, Jul 08 2008

%e O.g.f.: A(x) = 1 + x + 3*x^2 + 25*x^3 + 697*x^4 + 87261*x^5 + 63362851*x^6 +...

%e exp(x*A(x)) = 1 + x + 3*x^2/2! + 25*x^3/3! + 697*x^4/4! + 87261*x^5/5! + 63362851*x^6/6! +...

%o (PARI) {a(n)=local(E=1+x+x*O(x^n),F); for(j=0,n,F=exp(x*E);E=sum(i=0,n,polcoeff(F,i)*i!*x^i));polcoeff(E,n)}

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 27 2007