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A321386 a(n) = Sum_{d|n} (-1)^(n/d+1)*d^(d-1). 1
1, 1, 10, 61, 626, 7768, 117650, 2097085, 43046731, 999999376, 25937424602, 743008362964, 23298085122482, 793714773136496, 29192926025391260, 1152921504604749757, 48661191875666868482, 2185911559738653493015, 104127350297911241532842, 5242879999999998999999436, 278218429446951548637314060 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..21.

FORMULA

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

a(n) ~ n^(n-1). - Vaclav Kotesovec, Nov 09 2018

MATHEMATICA

Table[Sum[(-1)^(n/d + 1) d^(d - 1), {d, Divisors[n]}], {n, 21}]

nmax = 21; Rest[CoefficientList[Series[Sum[k^(k - 1) x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]

PROG

(PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1)*d^(d-1)); \\ Michel Marcus, Nov 09 2018

CROSSREFS

Cf. A000169, A262843, A321388.

Sequence in context: A319965 A025574 A301383 * A015867 A297863 A298130

Adjacent sequences:  A321383 A321384 A321385 * A321387 A321388 A321389

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 08 2018

STATUS

approved

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Last modified August 5 07:25 EDT 2020. Contains 336209 sequences. (Running on oeis4.)