A358607 -id:A358607 - cp's OEIS frontend

A358608 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-3*k)!.

1, 1, 2, 5, 23, 118, 715, 5017, 40202, 362165, 3623783, 39876598, 478639435, 6223397017, 87138414602, 1307195728565, 20916566490983, 355600289681398, 6401066509999435, 121624183842341017, 2432546407886958602, 51084541105199440565, 1123879103593765338983

Offset: 0

Seiichi Manyama, Nov 23 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..449

Cf. A358607, A358609, A358611.

Cf. A143630, A358498.

PARI
```
a(n) = sum(k=0, n\3, (-1)^k*(n-3*k)!);
```

a(n) = n * a(n-1) - a(n-3) + n * a(n-4) for n > 3.

a(n) ~ n! * (1 - 1/n^3 - 3/n^4 - 7/n^5 - 14/n^6 - 16/n^7 + 77/n^8 + 922/n^9 + 6660/n^10 + ...), for coefficients see A143630. - Vaclav Kotesovec, Nov 25 2022

A358609 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-4*k)!.

Original entry on oeis.org

1, 1, 2, 6, 23, 119, 718, 5034, 40297, 362761, 3628082, 39911766, 478961303, 6226658039, 87174663118, 1307634456234, 20922310926697, 355681201437961, 6402286531064882, 121643792774375766, 2432881085865713303, 51090586490508002039, 1123994325491076615118

Offset: 0

Seiichi Manyama, Nov 23 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..449

Cf. A358607, A358608, A358611.

Cf. A358499.

PARI
```
a(n) = sum(k=0, n\4, (-1)^k*(n-4*k)!);
```

a(n) = n * a(n-1) - a(n-4) + n * a(n-5) for n > 4.

a(n) ~ n! * (1 - 1/n^4 - 6/n^5 - 25/n^6 - 90/n^7 - 300/n^8 - 938/n^9 - 2563/n^10 - ...). - Vaclav Kotesovec, Nov 25 2022

A358611 a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (n-5*k)!.

Original entry on oeis.org

1, 1, 2, 6, 24, 119, 719, 5038, 40314, 362856, 3628681, 39916081, 478996562, 6226980486, 87177928344, 1307670739319, 20922749971919, 355686949099438, 6402367478747514, 121645013230903656, 2432900700505900681, 51090921248959468081, 1124000372090658580562

Offset: 0

Seiichi Manyama, Nov 23 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..449

Cf. A358607, A358608, A358609.

Cf. A358500.

PARI
```
a(n) = sum(k=0, n\5, (-1)^k*(n-5*k)!);
```

a(n) = n * a(n-1) - a(n-5) + n * a(n-6) for n > 5.

cp's OEIS Frontend

A358608 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-3*k)!.

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A358609 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-4*k)!.

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Formula

A358611 a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (n-5*k)!.

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