A143921 - OEIS

%I #7 Jul 30 2014 15:24:18

%S 1,1,3,10,49,281,1975,15933,147457,1528282,17603351,222691261,

%T 3072168481,45882929925,737717712439,12703639993306,233281370579713,

%U 4550465650811445,93966210612477271,2047838398486924977

%N E.g.f. A(x) satisfies: A(x) = exp(x + x*Integral A(x) dx).

%C Limit n->infinity (a(n)/n!)^(1/n) = 1.1453530527... - _Vaclav Kotesovec_, Feb 24 2014

%C Compare to: G(x) = exp(Integral G(x) dx) when G(x) = 1/(1-x).

%H Vaclav Kotesovec, <a href="/A143921/b143921.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f. A(x) satisfies: log(A(x)) = x*A'(x)/A(x) - x^2*A(x).

%e E.g.f. A(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 49*x^4/4! + 281*x^5/5! +...

%e log(A(x)) = x + x^2 + x^3/2! + 3*x^4/3! + 10*x^5/4! + 49*x^6/5! +...

%e A'(x)/A(x) = 1 + 2*x + 3*x^2/2! + 12*x^3/3! + 50*x^4/4! + 294*x^5/5! +...

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

%o for(n=0,25,print1(a(n),", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 06 2008