A356661 -id:A356661 - cp's OEIS frontend

A356662 a(n) = n! * Sum_{d|n} 1/(d!)^(n/d - 1).

1, 4, 12, 60, 240, 1740, 10080, 87360, 735840, 7514640, 79833600, 976686480, 12454041600, 175736040480, 2616448554720, 42011071502400, 711374856192000, 12830610027755520, 243290200817664000, 4870565189425615680, 102182981410948838400, 2249099140674523737600

Offset: 1

Seiichi Manyama, Aug 21 2022

nonn

Cf. A061095, A098558, A356543, A356661.

a[n_] := n! * DivisorSum[n, 1/(#!)^(n/# - 1) &]; Array[a, 22] (* Amiram Eldar, Aug 21 2022 *)

PARI
```
a(n) = n!*sumdiv(n, d, 1/d!^(n/d-1));
```

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(1-x^k/k!))))

a(p) = 2 * p! for prime p.

E.g.f.: Sum_{k>=1} x^k/(1 - x^k/k!).

A351165 a(n) = n! * Sum_{d|n} d^(d - n/d).

Original entry on oeis.org

1, 6, 60, 1584, 75120, 5601960, 592956000, 84557864160, 15620794842240, 3628800457682400, 1035338990353113600, 355902198996315787200, 145077660657865961625600, 69194697633957032681544000, 38174841090323471644830720000, 24122334398251368151021076928000

Offset: 1

Seiichi Manyama, Aug 21 2022

nonn

Cf. A062796, A087905, A355669, A356661.

a[n_] := n! * DivisorSum[n, #^(# - n/#) &]; Array[a, 16] (* Amiram Eldar, Aug 21 2022 *)

PARI
```
a(n) = n!*sumdiv(n, d, d^(d-n/d));
```

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k-x^k))))

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

cp's OEIS Frontend

A356662 a(n) = n! * Sum_{d|n} 1/(d!)^(n/d - 1).

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A351165 a(n) = n! * Sum_{d|n} d^(d - n/d).

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Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula