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A360175
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a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!) * [x^n] (1 - exp(-LambertW(x*exp(-x))))^k.
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0
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1, 1, 6, 53, 647, 10092, 191915, 4309769, 111682044, 3281731611, 107860953795, 3921762633846, 156322429050397, 6779458454252941, 317841794915501862, 16020304439710056785, 863955306007083830051, 49641711131738762890764, 3027776406780183894833791, 195382900651186641677702197
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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} |A360176(n, k)|.
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MAPLE
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egf := k -> (1 - exp(-LambertW(x*exp(-x))))^k / k!:
ser := k -> series(egf(k), x, 22):
T := (n, k) -> (-1)^(n-k)*n!*coeff(ser(k), x, n):
seq(add(T(n, k), k = 0..n), n = 0..19);
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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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