3 deleted 13 characters in body
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Another approach, using Inner:

Edit

As per J.M's comment above regarding Table:

s // Inner[Table, #, RotateLeft@#, List] &

(As per J.M's comment above regarding Table)

Original Post

s // Inner[NestList[# &, #1, #2 - 1] &, #, RotateLeft@#, List] &

{{3, 3, 3, 3}, {4, 4, 4, 4, 4, 4}, {6}, {1, 1}, {2, 2, 2, 2, 2}, {5, 5, 5}}

Alternatively:

s // Inner[ConstantArray, #, RotateLeft@#, List] &

Another approach, using Inner:

Edit

As per J.M's comment above regarding Table:

s // Inner[Table, #, RotateLeft@#, List] &

Original Post

s // Inner[NestList[# &, #1, #2 - 1] &, #, RotateLeft@#, List] &

{{3, 3, 3, 3}, {4, 4, 4, 4, 4, 4}, {6}, {1, 1}, {2, 2, 2, 2, 2}, {5, 5, 5}}

Alternatively:

s // Inner[ConstantArray, #, RotateLeft@#, List] &

Another approach, using Inner:

s // Inner[Table, #, RotateLeft@#, List] &

(As per J.M's comment above regarding Table)

Original Post

s // Inner[NestList[# &, #1, #2 - 1] &, #, RotateLeft@#, List] &

{{3, 3, 3, 3}, {4, 4, 4, 4, 4, 4}, {6}, {1, 1}, {2, 2, 2, 2, 2}, {5, 5, 5}}

Alternatively:

s // Inner[ConstantArray, #, RotateLeft@#, List] &
2 add Table solution
source | link

Another approach, using InnerInner:

Edit

As per J.M's comment above regarding Table:

s // Inner[Table, #, RotateLeft@#, List] &

Original Post

s // Inner[NestList[# &, #1, #2 - 1] &, #, RotateLeft@#, List] &

{{3, 3, 3, 3}, {4, 4, 4, 4, 4, 4}, {6}, {1, 1}, {2, 2, 2, 2, 2}, {5, 5, 5}}

Alternatively:

s // Inner[ConstantArray, #, RotateLeft@#, List] &

Another approach, using Inner:

s // Inner[NestList[# &, #1, #2 - 1] &, #, RotateLeft@#, List] &

{{3, 3, 3, 3}, {4, 4, 4, 4, 4, 4}, {6}, {1, 1}, {2, 2, 2, 2, 2}, {5, 5, 5}}

Alternatively:

s // Inner[ConstantArray, #, RotateLeft@#, List] &

Another approach, using Inner:

Edit

As per J.M's comment above regarding Table:

s // Inner[Table, #, RotateLeft@#, List] &

Original Post

s // Inner[NestList[# &, #1, #2 - 1] &, #, RotateLeft@#, List] &

{{3, 3, 3, 3}, {4, 4, 4, 4, 4, 4}, {6}, {1, 1}, {2, 2, 2, 2, 2}, {5, 5, 5}}

Alternatively:

s // Inner[ConstantArray, #, RotateLeft@#, List] &
1
source | link

Another approach, using Inner:

s // Inner[NestList[# &, #1, #2 - 1] &, #, RotateLeft@#, List] &

{{3, 3, 3, 3}, {4, 4, 4, 4, 4, 4}, {6}, {1, 1}, {2, 2, 2, 2, 2}, {5, 5, 5}}

Alternatively:

s // Inner[ConstantArray, #, RotateLeft@#, List] &