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A163191
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a(n) = Sum_{k=0..n} (-1)^(n-k)*C(n,k)*sigma(n,k) for n>0 with a(0)=1.
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3
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1, 0, 1, 8, 82, 1024, 15690, 279936, 5771363, 134218240, 3487832978, 100000000000, 3138673052884, 106993205379072, 3937454749863386, 155568096631586816, 6568441588686506948, 295147905179352825856, 14063102470280932000763, 708235345355337676357632
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OFFSET
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0,4
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COMMENTS
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Definition: sigma(n,k)= sigma_k(n) = Sum_{d|n} d^k.
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LINKS
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FORMULA
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a(n) = Sum_{d|n} (d-1)^n for n>0 with a(0)=1.
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MATHEMATICA
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a[0] = 1; a[n_] := DivisorSum[n, (#-1)^n &]; Array[a, 20, 0] (* Amiram Eldar, Aug 15 2023 *)
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PROG
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(PARI) {a(n)=if(n==0, 1, sumdiv(n, d, (d-1)^n))}
(PARI) {a(n)=if(n==0, 1, sum(k=0, n, (-1)^(n-k)*binomial(n, k)*sigma(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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