A392321 Number of all 1-tuples, 2-tuples, ..., n-tuples where each entry is chosen from the nonempty subsets of {1,..,n}.

1, 12, 399, 54240, 29583455, 63531945792, 537105033658879, 17948489581465697280, 2380339071283027535464959, 1256553762866594861176299973632, 2645504365809312169291790270859325439, 22240929882283139632635951344835218632581120

Offset

1,2

Links

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

Formula

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

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

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

For n > 1, a(n) = ((2^n - 1)^(n+1) - 1)/(2^n - 2) - 1. - Vaclav Kotesovec, Jan 21 2026

Example

The a(2) = 3 + 9 = 12:
   ({1})    ({1},{1})
   ({2})    ({1},{2})
   ({1,2})  ({1},{1,2})
            ({2},{1})
            ({2},{2})
            ({2},{1,2})
            ({1,2},{1})
            ({1,2},{2})
            ({1,2},{1,2})

Mathematica

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

Crossrefs

Cf. A329943, A245789.

Sequence in context: A286038 A276482 A202788 * A285028 A292784 A003772

Adjacent sequences: A392318 A392319 A392320 * A392322 A392323 A392324

Keyword

nonn,easy

Author

Rajesh Kumar Mohapatra, Jan 10 2026

Status

approved