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A168603
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G.f. satisfies: A(x) = 1 + x*A(x)^2*A(2x)^2.
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1
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1, 1, 6, 73, 1578, 60582, 4276284, 574950725, 150783454338, 78124426877002, 80472666325118724, 165293072210433580170, 678034405564452384600036, 5558530569192415381768200652, 91104334435045362173635840712184
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ c * 2^(n*(n+1)/2)), where c = 2.246717964359561210869708946140382812767... - Vaclav Kotesovec, Nov 13 2021
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EXAMPLE
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G.f.: A(x) = 1 + x + 6*x^2 + 73*x^3 + 1578*x^4 + 60582*x^5 +...
A(x)^2 = 1 + 2*x + 13*x^2 + 158*x^3 + 3338*x^4 + 125196*x^5 +...
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MATHEMATICA
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nmax = 20; A[_] = 0; Do[A[x_] = 1 + x*A[x]^2*A[2*x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 13 2021 *)
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PROG
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*A^2*subst(A, x, 2*x)^2 ); 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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