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a(n) = coefficient of x^n in the (2^(n-1))-th iteration of x*C(x) where C(x) is the Catalan function (A000108), for n>=1.
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%I #2 Mar 30 2012 18:37:16

%S 1,2,20,684,84864,40783952,78562790592,613738473236928,

%T 19459342629747109248,2496653806284295319455488,

%U 1291725241770954532057108070400,2687434858858114549619735481969223680

%N a(n) = coefficient of x^n in the (2^(n-1))-th iteration of x*C(x) where C(x) is the Catalan function (A000108), for n>=1.

%o (PARI) {a(n)=local(G=serreverse(x-x^2+O(x^(n+2))));for(i=2,n,G=subst(G,x,G));polcoeff(G,n)}

%Y Cf. A158269, A000108, A158825.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Mar 28 2009