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A185524 a(n) equals the coefficient of x^n in the (n+1)-th iteration of x*(1+x)/(1-x) for n>=1.

%I A185524 #4 Mar 30 2012 18:37:25
%S A185524 1,6,56,770,14272,335846,9623280,325812162,12743851808,565954103110,
%T A185524 28147009533480,1550288951887650,93697417382512608,
%U A185524 6166356881177224390,439006462312153564128,33620884878446290152706,2756259421284677015952320
%N A185524  a(n) equals the coefficient of x^n in the (n+1)-th iteration of x*(1+x)/(1-x) for n>=1.
%e A185524  Given G(x) = x*(1+x)/(1-x):
%e A185524 G(x) = x + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 2*x^6 +...
%e A185524 then the initial coefficients of the n-th iterations of G(x) begin:
%e A185524 n=1: [1, 2, 2, 2, 2, 2, 2, 2, 2, ...];
%e A185524 n=2: [(1), 4, 12, 32, 80, 196, 476, 1152, 2784, ...];
%e A185524 n=3: [1,(6), 30, 138, 602, 2542, 10518, 42994, ...];
%e A185524 n=4: [1, 8,(56), 368, 2320, 14216, 85368, 505312, ...];
%e A185524 n=5: [1, 10, 90,(770), 6370, 51450, 408202, 3194978, ...];
%e A185524 n=6: [1, 12, 132, 1392,(14272), 143372, 1418004, 13854368, ...];
%e A185524 n=7: [1, 14, 182, 2282, 27930,(335846), 3983518, 46736466, ...];
%e A185524 n=8: [1, 16, 240, 3488, 49632, 695312,(9623280), 131891776, ...];
%e A185524 n=9: [1, 18, 306, 5058, 82050, 1312626, 20771730,(325812162), ...]; ...;
%e A185524 the coefficients in parenthesis form the initial terms of this sequence.
%o A185524  (PARI) {a(n)=local(A=x,G=x*(1+x)/(1-x+x*O(x^n))); for(i=1, n+1, A=subst(G, x, A+x*O(x^n))); polcoeff(A, n)}
%Y A185524  Cf. A185522, A185523.
%K A185524 nonn
%O A185524 1,2
%A A185524 _Paul D. Hanna_, Jan 30 2011