A354891
a(n) = n! * Sum_{d|n} d^(n - d) / d!.
Original entry on oeis.org
1, 3, 7, 73, 121, 9721, 5041, 1760641, 44452801, 562615201, 39916801, 3156125575681, 6227020801, 192873372531841, 222245415808416001, 14806216643368550401, 355687428096001, 34884164976924636172801, 121645100408832001
Offset: 1
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a[n_] := n! * DivisorSum[n, #^(n - #)/#! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)
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a(n) = n!*sumdiv(n, d, d^(n-d)/d!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k!*(1-(k*x)^k)))))
A354897
a(n) = n! * Sum_{d|n} d^n / (d! * (n/d)!).
Original entry on oeis.org
1, 5, 28, 353, 3126, 94237, 823544, 72042497, 585825130, 157671732881, 285311670612, 790577855833537, 302875106592254, 5876819345289651137, 55890419425648520176, 73205730667453550166017, 827240261886336764178, 1474631675630757976051079425
Offset: 1
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a[n_] := n! * DivisorSum[n, #^n/(#! * (n/#)!) &]; Array[a, 18] (* Amiram Eldar, Jun 11 2022 *)
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a(n) = n!*sumdiv(n, d, d^n/(d!*(n/d)!));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp((k*x)^k)-1)/k!)))
A354898
a(n) = n! * Sum_{d|n} d^(n - d) / (d! * (n/d)!).
Original entry on oeis.org
1, 2, 2, 26, 2, 2582, 2, 268802, 7348322, 51120722, 2, 299332756802, 2, 7157951760962, 18701679546950402, 613777679843328002, 2, 3250742570192384467202, 2, 29411516073133093829529602, 1146522800008167069616128002, 4017001663590220290585602, 2
Offset: 1
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f:= proc(n) local d; n! * add(d^(n-d)/(d! * (n/d)!), d = numtheory:-divisors(n)) end proc:
map(f, [$1..30]); # Robert Israel, Jul 10 2023
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a[n_] := n! * DivisorSum[n, #^(n - #)/(#! * (n/#)!) &]; Array[a, 23] (* Amiram Eldar, Jun 11 2022 *)
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a(n) = n!*sumdiv(n, d, d^(n-d)/(d!*(n/d)!));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp((k*x)^k)-1)/(k^k*k!))))
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