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A360176
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Triangle read by rows. T(n, k) = Sum_{j=k..n} binomial(n, j) * (-j)^(n - j) * (-1)^(j - k)* A360177(j, k).
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2
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1, 0, 1, 0, -5, 1, 0, 37, -15, 1, 0, -393, 223, -30, 1, 0, 5481, -3815, 745, -50, 1, 0, -95053, 76051, -18870, 1865, -75, 1, 0, 1975821, -1749811, 514381, -65730, 3920, -105, 1, 0, -47939601, 45876335, -15316854, 2358181, -183610, 7322, -140, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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E.g.f. of column k: (1 - exp(-LambertW(x*exp(-x))))^k / k!.
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EXAMPLE
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Triangle T(n, k) starts:
[0] 1;
[1] 0, 1;
[2] 0, -5, 1;
[3] 0, 37, -15, 1;
[4] 0, -393, 223, -30, 1;
[5] 0, 5481, -3815, 745, -50, 1;
[6] 0, -95053, 76051, -18870, 1865, -75, 1;
[7] 0, 1975821, -1749811, 514381, -65730, 3920, -105, 1;
[8] 0, -47939601, 45876335, -15316854, 2358181, -183610, 7322, -140, 1;
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MAPLE
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T := (n, k) -> add(binomial(n, j) * (-j)^(n - j) * (-1)^(j - k) * A360177(j, k), j = k..n): for n from 0 to 9 do seq(T(n, k), k = 0..n) od;
# Alternative:
egf := k -> (1 - exp(-LambertW(x*exp(-x))))^k / k!:
ser := k -> series(egf(k), x, 22): T := (n, k) -> n!*coeff(ser(k), x, n):
for n from 0 to 8 do seq(T(n, k), k = 0..n) od;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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