A392322 Number of coverings of [n] by 1-tuples, 2-tuples, ..., n-tuples where each entry is chosen from the subsets of [n].

1, 10, 371, 53108, 29405577, 63422514894, 536842525103887, 17946027593293876456, 2380248400260600171166613, 1256540596610637930077566092098, 2645496803167571992523450535629589723, 22240912657758659268957594752722686275423964

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Formula

a(n) = Sum_{k=1..n} (2^k - 1)^n.

a(n) = Sum_{k=1..n} A092477(n,k).

a(n) = Sum_{k=1..n} A329943(k,n).

a(n) = Sum_{k=1..n} A245789(n,k).

Example

The a(2) = 1 + 9 = 10:
   ({1,2})  ({},{1,2})
            ({1},{2})
            ({1},{1,2})
            ({2},{1,2})
            ({2},{1})
            ({1,2},{})
            ({1,2},{1})
            ({1,2},{2})
            ({1,2},{1,2}).

Mathematica

a[n_] := a[n] = Sum[(2^k - 1)^n, {k, 1, n}]; Table[a[n], {n, 1, 15}]

Crossrefs

Cf. A092477, A329943, A245789, A392321.

Sequence in context: A119547 A117797 A301311 * A291530 A358801 A381185

Adjacent sequences: A392319 A392320 A392321 * A392323 A392324 A392326

Keyword

nonn

Author

Rajesh Kumar Mohapatra and Ranjan Kumar Dhani, Jan 21 2026

Status

approved