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A331726
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E.g.f.: -LambertW(-x/(1 - x)) / (1 - x).
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3
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0, 1, 6, 45, 448, 5825, 95796, 1926043, 45944256, 1269187137, 39840825700, 1400286658331, 54462564354672, 2321934762267601, 107664031299459012, 5393893268767761675, 290341440380472614656, 16710435419661861992705, 1024009456958258244673860
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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) = Sum_{k=0..n-1} binomial(n,k)^2 * k! * (n - k)^(n - k - 1).
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MATHEMATICA
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nmax = 18; CoefficientList[Series[-LambertW[-x/(1 - x)]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k]^2 k! (n - k)^(n - k - 1), {k, 0, n - 1}], {n, 0, 18}]
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PROG
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(PARI) seq(n)={Vec(serlaplace(-lambertw(-x/(1 - x) + O(x*x^n)) / (1 - x)), -(n+1))} \\ Andrew Howroyd, Jan 25 2020
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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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