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A362492
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E.g.f. satisfies A(x) = exp(x - x^2/2 * A(x)^2).
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4
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1, 1, 0, -8, -38, 106, 3676, 24508, -296036, -9149156, -56500064, 2211573376, 64958496472, 184823374360, -35372361487280, -971135892546224, 4364710018963216, 1034808592156017424, 25290798052846014208, -474242641154857953152, -49625273567646267051104
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: exp(x - LambertW(x^2 * exp(2*x))/2) = sqrt( LambertW(x^2 * exp(2*x))/x^2 ).
a(n) = n! * Sum_{k=0..floor(n/2)} (-1/2)^k * (2*k+1)^(n-k-1) / (k! * (n-2*k)!).
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MAPLE
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N:= 50: # for a(0)..a(N)
egf:= exp(x - LambertW(x^2 * exp(2*x))/2):
S:=series(egf, x, N+1):
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^2*exp(2*x))/2)))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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