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A322626
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G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * (n - A(x)^n)^n.
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1
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1, 1, 4, 31, 362, 5567, 104229, 2268586, 55817457, 1524956611, 45699911560, 1489007130546, 52390324106713, 1979726546053502, 79978929224189504, 3440756672193895992, 157085559415640319126, 7587124626671398460006, 386598739562989187413005, 20728976430148069600767400, 1166849728839227202686314988
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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 * n^(n+1), where c = 0.6410371541108... - Vaclav Kotesovec, Aug 11 2021
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EXAMPLE
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G.f.: A(x) = 1 + x + 4*x^2 + 31*x^3 + 362*x^4 + 5567*x^5 + 104229*x^6 + 2268586*x^7 + 55817457*x^8 + 1524956611*x^9 + 45699911560*x^10 + ...
such that
1 = 1 + x*(1 - A(x)) + x^2*(2 - A(x)^2)^2 + x^3*(3 - A(x)^3)^3 + x^4*(4 - A(x)^4)^4 + x^5*(5 - A(x)^5)^5 + x^6*(6 - A(x)^6)^6 + ...
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PROG
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(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = Vec(sum(m=0, #A, x^m*(m - Ser(A)^m)^m))[#A+1]); A[n+1]}
for(n=0, 25, print1(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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