A221835 - OEIS

%I #9 Feb 22 2013 21:51:19

%S 1,1,1,1,2,2,5,7,23,48,190,469,2076,5613,27112,80004,415821,1332560,

%T 7380671,25483465,149401274,552137511,3408722899,13414205244,

%U 86845091349,362317409552,2451291749604,10800354549538,76134098052646,353054546986058,2586405677507199

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (x + A(-x)^k).

%C Compare to the identity:

%C G(x) = Sum_{n>=0} x^n / Product_{k=1..n} (x + G(-k*x)) when G(x) = 1/(1-x).

%e G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 2*x^5 + 5*x^6 + 7*x^7 + 23*x^8 +...

%e where

%e A(x) = 1 + x/(x+A(-x)) + x^2/((x+A(-x))*(x+A(-x)^2)) + x^3/((x+A(-x))*(x+A(-x)^2)*(x+A(-x)^3)) + x^4/((x+A(-x))*(x+A(-x)^2)*(x+A(-x)^3)*(x+A(-x)^4)) +...

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

%o for(n=0, 40, print1(a(n), ", "))

%K nonn

%O 0,5

%A _Paul D. Hanna_, Feb 22 2013