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A349969
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a(n) = Sum_{k=0..n} (k*n)^(n-k).
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3
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1, 1, 3, 16, 141, 1871, 34951, 873174, 27951929, 1107415549, 52891809491, 2987861887924, 196828568831365, 14950745148070499, 1296606974501951743, 127238563043551898986, 14012626653816435643633, 1719136634276882827095009, 233448782800118609096218891
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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) = [x^n] Sum_{k>=0} x^k/(1 - n*k * x).
a(n) ~ sqrt(2*Pi/(n*(1 + LambertW(exp(1)*n^2)))) * (n^2/LambertW(exp(1)*n^2))^(n + 1/2 - n/LambertW(exp(1)*n^2)). - Vaclav Kotesovec, Dec 07 2021
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MATHEMATICA
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a[n_] := Sum[If[k == n == 0, 1, (k*n)^(n - k)], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Dec 07 2021 *)
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PROG
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(PARI) a(n) = sum(k=0, n, (k*n)^(n-k));
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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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