A181445 - OEIS

%I #4 Jan 16 2013 20:24:09

%S 1,1,2,10,110,2468,110678,9893848,1765620796,629689184768,

%T 449004143002080,640244024341490536,1825757754872909135396,

%U 10412557570967501281794528,118766811331255795668894586000

%N G.f. satisfies: A(x) = Sum_{n>=0} log(1 + x*A(2^n*x))^n/n!.

%F G.f. satisfies: A(x) = Sum_{n>=0} x^n * Sum_{k=0..n} Stirling1(n,k) * A(2^k*x)^n/n!. - _Paul D. Hanna_, Jan 16 2013

%e G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 110*x^4 + 2468*x^5 +...

%e A(x) = 1 + log(1+x*A(2*x)) + log(1+x*A(4*x))^2/2! + log(1+x*A(8*x))^3/3! + log(1+x*A(16*x))^4/4! + log(1+x*A(32*x))^5/5! +...

%o (PARI) {a(n)=local(A=1+sum(m=1,n-1,a(m)*x^m));polcoeff(sum(m=0,n,log(1+x*subst(A,x,2^m*x)+x*O(x^n))^m/m!),n)}

%o (PARI) {Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}

%o {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, sum(k=0, m, Stirling1(m, k)*subst(A, x, 2^k*x+x*O(x^n))^m)*x^m/m!)); n!*polcoeff(A, n)}

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A132695.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 20 2010