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A162287
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G.f. satisfies: A(x) = exp( Sum_{n>=1} [Sum{d|n} A(2^d*n*x/d)^d/d]*x^n ).
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0
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1, 1, 4, 29, 417, 11629, 635575, 68495847, 14649466838, 6240047796536, 5303983470442186, 9004906378193235074, 30552213347609385960757, 207213131514991438965771387, 2809810971676044211903643478219
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..14.
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EXAMPLE
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G.f.: A(x) = 1 + x + 4*x^2 + 29*x^3 + 417*x^4 + 11629*x^5 +...
log(A(x)) = A(2*x)*x + [A(2*2x) + A(2^2*x)^2/2]*x^2 + [A(2*3x) + A(2^3*x)^3/3]*x^3 + [A(2*4x) + A(2^2*2x)^2/2 + A(2^4*x)^4/4]*x^4 +...
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sumdiv(m, d, m*subst(A, x, 2^d*m*x/d+x*O(x^n))^d/d)*x^m/m))); polcoeff(A, n)}
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CROSSREFS
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Cf. A162286.
Sequence in context: A135485 A210526 A221079 * A173715 A166168 A126559
Adjacent sequences: A162284 A162285 A162286 * A162288 A162289 A162290
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Jun 29 2009
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STATUS
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approved
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