A356013 -id:A356013 - cp's OEIS frontend

A356011 a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)).

1, 2, 6, 17, 80, 337, 2240, 14681, 117010, 1023941, 10900472, 108881665, 1375544846, 17732140805, 247041590476, 3605768497217, 59990390084690, 977383707751621, 18214603019184800, 337615168055209601, 6763842079452393622, 141262515443311046885

Offset: 1

Seiichi Manyama, Jul 23 2022

nonn

Row sums of A356013.

Cf. A345682, A345683, A355991, A356015.

Table[n! * Sum[1/(k!*Floor[n/k]), {k,1,n}], {n,1,25}] (* Vaclav Kotesovec, Aug 11 2025 *)

PARI
```
a(n) = n!*sum(k=1, n, 1/(k!*(n\k)));
```

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

E.g.f.: -(1/(1-x)) * Sum_{k>0} (1 - x^k) * log(1 - x^k)/k!.

a(n) ~ exp(1) * (n-1)!. - Vaclav Kotesovec, Aug 11 2025

A356012 a(n) = n! / (6 * floor(n/3)).

Original entry on oeis.org

1, 4, 20, 60, 420, 3360, 20160, 201600, 2217600, 19958400, 259459200, 3632428800, 43589145600, 697426329600, 11856247603200, 177843714048000, 3379030566912000, 67580611338240000, 1216451004088320000, 26761922089943040000, 615524208068689920000

Offset: 3

Seiichi Manyama, Jul 23 2022

Column 3 of A356013.

Cf. A355990.

Table[n!/(6 Floor[n/3]),{n,3,30}] (* Harvey P. Dale, Jul 25 2024 *)

PARI
```
a(n) = n!/(6*(n\3));
```

my(N=30, x='x+O('x^N)); Vec(serlaplace(-(1-x^3)*log(1-x^3)/(6*(1-x))))

E.g.f.: -(1 - x^3) * log(1 - x^3)/(6 * (1 - x)).

cp's OEIS Frontend

A356011 a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)).

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Mathematica

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A356012 a(n) = n! / (6 * floor(n/3)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula