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A168602
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G.f. satisfies: A(x) = 1 + x*A(x)^2*A(2x).
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2
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1, 1, 4, 29, 348, 7078, 257400, 17567085, 2321150956, 603642816242, 311497277686152, 320223587003352866, 657101019781977963480, 2694116441965648648689708, 22080982977564915182409980400
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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(0) = 1; a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-1} 2^i * a(i) * a(j) * a(n-i-j-1). - Ilya Gutkovskiy, Nov 12 2021
a(n) ~ c * 2^(n*(n-1)/2)), where c = 8.922794036651587033803872123786584213844... - Vaclav Kotesovec, Nov 13 2021
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EXAMPLE
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G.f.: A(x) = 1 + x + 4*x^2 + 29*x^3 + 348*x^4 + 7078*x^5 +...
A(x)^2 = 1 + 2*x + 9*x^2 + 66*x^3 + 770*x^4 + 15084*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] + 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) ); 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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