A088715 - OEIS

%I #13 Jul 19 2016 10:53:18

%S 1,1,2,7,36,240,1926,17815,184916,2116498,26391700,355405934,

%T 5134778584,79178537346,1297633495518,22522717498167,412754532495252,

%U 7965288555078018,161475849044919996,3431346397643014818

%N G.f. satisfies: A(x*g(x)) = g(x) where g(x) is the g.f. of A088716.

%H Vaclav Kotesovec, <a href="/A088715/b088715.txt">Table of n, a(n) for n = 0..440</a>

%F G.f.: Coefficient of x^n in A(x)^(n+1)/(n+1) = coefficient of x^n in A(x)^(n+2) = A088716(n).

%F G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/(1 - x*[A'(x)/A(x)])^n/n ). - _Paul D. Hanna_, Aug 31 2009

%F G.f. satisfies: A(x) = 1 + x*A(x)^2/(A(x) - x*A'(x)). - _Paul D. Hanna_, Mar 20 2013

%F a(n) ~ c * n! * n^2, where c = A238223 / exp(1) = 0.08017961462469262235245081077906956577... - _Vaclav Kotesovec_, Feb 21 2014

%o (PARI) a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=exp(sum(k=1,n,(1-x*deriv(log(A)))^(-k)*x^k/k)));polcoeff(A,n) \\ _Paul D. Hanna_, Aug 31 2009

%o (PARI) a(n)=local(A=1+x); for(i=1, n, A=1+x*A^2/(A-x*deriv(A)+x*O(x^n))); polcoeff(A, n)

%o for(n=0,30,print1(a(n),", ")) \\ _Paul D. Hanna_, Mar 20 2013

%Y Cf. A088716, A238223.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 12 2003