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A362694
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E.g.f. satisfies A(x) = exp(x + x * A(x)^2).
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7
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1, 2, 12, 152, 2960, 78112, 2607808, 105432448, 5008584960, 273482293760, 16878251101184, 1161918967060480, 88277165100666880, 7337286679766179840, 662287143981044121600, 64516370031367063175168, 6746443728505612426870784, 753763691778003738319519744
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: sqrt( -LambertW(-2*x*exp(2*x)) / (2*x) ) = exp( x - LambertW(-2*x*exp(2*x))/2 ).
a(n) = Sum_{k=0..n} (2*k+1)^(n-1) * binomial(n,k) = 2^n * A202617(n).
a(n) ~ sqrt(1 + 1/LambertW(exp(-1))) * 2^(n-1) * n^(n-1) / (exp(n) * LambertW(exp(-1))^n). - Vaclav Kotesovec, Nov 10 2023
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-2*x*exp(2*x))/2)))
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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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