A343568 a(n) = Sum_{d|n} (n/d)^(n/d) * binomial(d+n-1,n).
1, 7, 37, 311, 3251, 47419, 825259, 16786615, 387446284, 10000130757, 285312023327, 8916102467195, 302875111792553, 11112006858124501, 437893890458947787, 18446744074296533175, 827240261887503567287, 39346408075308452154628
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^(n/#) * Binomial[# + n - 1, n] &]; Array[a, 20] (* Amiram Eldar, Apr 25 2021 *)
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PARI
a(n) = sumdiv(n, d, (n/d)^(n/d)*binomial(d+n-1, n));
Formula
a(n) = [x^n] Sum_{k>=1} (k * x)^k/(1 - x^k)^(n+1).