A338683 - OEIS

A338683

a(n) = - Sum_{d|n} (-n/d)^d * binomial(d+n/d-1, d).

1, 3, 10, 3, 26, 13, 50, -177, 352, -84, 122, -996, 170, -153, 9704, -13313, 290, -6518, 362, -2771, 107986, 17073, 530, -805070, 394376, 99984, 1203580, 1196313, 842, -4500745, 962, -13313025, 14199222, 2316234, 33547310, -19898071, 1370, 10418613, 168405072

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..39.

FORMULA

G.f.: Sum_{k >= 1} (1 - 1/(1 + k * x^k)^k).

If p is prime, a(p) = (-1)^(p-1) + p^2.

MATHEMATICA

a[n_] := -DivisorSum[n, (-n/#)^# * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* Amiram Eldar, Apr 24 2021 *)

PROG

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