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A362348
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a(n) = n! * Sum_{k=0..floor(n/3)} k^k / (k! * (n-3*k)!).
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7
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1, 1, 1, 7, 25, 61, 1561, 10291, 40657, 1754425, 16632721, 90479071, 5469933481, 67591594357, 468224398825, 36386954606731, 554182030325281, 4663003095358321, 442756825853252257, 8014853488848923575, 79354642490200806841, 8901962495566386752941
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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) / (1 + LambertW(-x^3)).
a(n) ~ (exp(3*exp(-1/3)/2) + 2*cos(sqrt(3)*exp(-1/3)/2 - 2*Pi*n/3)) * n^n / (sqrt(3) * exp(2*n/3 + exp(-1/3)/2)). - Vaclav Kotesovec, Apr 18 2023
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^3))))
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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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