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A351165
a(n) = n! * Sum_{d|n} d^(d - n/d).
1
1, 6, 60, 1584, 75120, 5601960, 592956000, 84557864160, 15620794842240, 3628800457682400, 1035338990353113600, 355902198996315787200, 145077660657865961625600, 69194697633957032681544000, 38174841090323471644830720000, 24122334398251368151021076928000
OFFSET
1,2
FORMULA
E.g.f.: Sum_{k>=1} (k * x)^k/(k - x^k).
MATHEMATICA
a[n_] := n! * DivisorSum[n, #^(# - n/#) &]; Array[a, 16] (* Amiram Eldar, Aug 21 2022 *)
PROG
(PARI) a(n) = n!*sumdiv(n, d, d^(d-n/d));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k-x^k))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 21 2022
STATUS
approved