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G.f. satisfies: A(x) = Sum{n>=0} x^n * A(2*n*x).
0

%I #5 Mar 30 2012 18:37:28

%S 1,1,3,17,191,4261,189123,16723689,2949213319,1037964817357,

%T 729449200732395,1024041038817726353,2872628913886690237679,

%U 16105674069113302453209781,180504701103754829110217971731,4044484405239396750189431682523833

%N G.f. satisfies: A(x) = Sum{n>=0} x^n * A(2*n*x).

%F a(n) = Sum_{k=0..n-1} 2^k*(n-k)^k * a(k) for n>0 with a(0)=1.

%e G.f.: A(x) = 1 + x + 3*x^2 + 17*x^3 + 191*x^4 + 4261*x^5 +...

%e where:

%e A(x) = 1 + x*A(2*x) + x^2*A(4*x) + x^3*A(6*x) + x^4*A(8*x) + x^5*A(10*x) +...

%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*subst(A,x,2*j*x))); polcoeff(A, n)}

%o (PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, 2^k*(n-k)^k*a(k)))}

%Y Cf. A125282.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 08 2011