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A205501
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G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Product_{d|n} A(d*x^d)^n ).
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4
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1, 1, 2, 5, 16, 50, 177, 608, 2205, 7948, 29552, 109554, 414342, 1568627, 6011290, 23102857, 89512855, 347930789, 1360252177, 5334715764, 21012372520, 83004307780, 328996301835, 1307386952248, 5209629950774, 20806467497993, 83287927579183, 334066903101026
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OFFSET
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0,3
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LINKS
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EXAMPLE
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G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 50*x^5 + 177*x^6 + 608*x^7 +...
By definition:
log(A(x)) = x*A(x) + x^2*A(x)^2*A(2*x^2)^2/2 + x^3*A(x)^3*A(3*x^3)^3/3 + x^4*A(x)^4*A(2*x^2)^4*A(4*x^4)^4/4 + x^5*A(x)^5*A(5*x^5)^5/5 + x^6*A(x)^6*A(2*x^2)^6*A(3*x^3)^6*A(6*x^6)^6/6 +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 156*x^5/5 + 672*x^6/6 + 2570*x^7/7 + 10619*x^8/8 + 41968*x^9/9 +...
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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, x^m/m*exp(sumdiv(m, d, log(subst(A^m, x, d*x^d +x*O(x^n)))))))); polcoeff(A, n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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