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A341056
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a(n) = n! * [x^n] exp(x/(1 - n*x)) / (1 - x).
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0
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1, 2, 9, 106, 2801, 132426, 9705577, 1015001954, 143392421601, 26298332570386, 6074043257989001, 1724846814877790682, 590605908915568818769, 239956225437223244619866, 114123836188192016600789481, 62808518765936960824453590226, 39603421893790601518269204039617
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..n} A341033(k,n)/k! = n! * (1 + Sum_{j=1.. n} Sum_{k=1.. j} n^(j-k) * binomial(j-1,k-1)/k!).
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EXAMPLE
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a(3) = 3! * (1 + 1/1! + 7/2! + 73/3!) = 106.
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MATHEMATICA
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Table[n!*(1 + Sum[Sum[n^(j-k)*Binomial[j-1, k-1]/k!, {k, 1, j}], {j, 1, n}]), {n, 0, 20}] (* Vaclav Kotesovec, Feb 14 2021 *)
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PROG
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(PARI) {a(n) = n!*(1+sum(j=1, n, sum(k=1, j, n^(j-k)*binomial(j-1, k-1)/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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