A343568 - OEIS

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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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n) = [x^n] Sum_{k>=1} (k * x)^k/(1 - x^k)^(n+1).

MATHEMATICA

a[n_] := DivisorSum[n, (n/#)^(n/#) * Binomial[# + n - 1, n] &]; Array[a, 20] (* Amiram Eldar, Apr 25 2021 *)

PROG

(PARI) a(n) = sumdiv(n, d, (n/d)^(n/d)*binomial(d+n-1, n));

CROSSREFS

Cf. A343549, A343567.

Sequence in context: A089677 A075996 A356127 * A173766 A093168 A330388

Adjacent sequences: A343565 A343566 A343567 * A343569 A343570 A343571

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 20 2021

STATUS

approved