A323775 a(n) = Sum_{k = 1...n} k^(2^(n - k)).

1, 3, 8, 30, 359, 72385, 4338080222, 18448597098193762732, 340282370354622283774333836315916425069, 115792089237316207213755562747271079374483128445080168204415615259394085515423

Offset

1,2

Comments

Number of ways to choose a constant integer partition of each part of a constant integer partition of 2^(n - 1).

Links

Table of n, a(n) for n=1..10.

Example

The a(1) = 1 through a(4) = 30 twice-partitions:
  (1)  (2)     (4)           (8)
       (11)    (22)          (44)
       (1)(1)  (1111)        (2222)
               (2)(2)        (4)(4)
               (11)(2)       (22)(4)
               (2)(11)       (4)(22)
               (11)(11)      (22)(22)
               (1)(1)(1)(1)  (1111)(4)
                             (4)(1111)
                             (11111111)
                             (1111)(22)
                             (22)(1111)
                             (1111)(1111)
                             (2)(2)(2)(2)
                             (11)(2)(2)(2)
                             (2)(11)(2)(2)
                             (2)(2)(11)(2)
                             (2)(2)(2)(11)
                             (11)(11)(2)(2)
                             (11)(2)(11)(2)
                             (11)(2)(2)(11)
                             (2)(11)(11)(2)
                             (2)(11)(2)(11)
                             (2)(2)(11)(11)
                             (11)(11)(11)(2)
                             (11)(11)(2)(11)
                             (11)(2)(11)(11)
                             (2)(11)(11)(11)
                             (11)(11)(11)(11)
                             (1)(1)(1)(1)(1)(1)(1)(1)

Mathematica

Table[Sum[k^2^(n-k), {k, n}], {n, 12}]

Crossrefs

Cf. A000123, A001970, A002577, A006171, A279787, A279789, A305551, A306017, A319056, A323766, A323774, A323776.

Sequence in context: A298456 A145776 A066165 * A360605 A119838 A148889

Adjacent sequences: A323772 A323773 A323774 * A323776 A323777 A323778

Keyword

nonn

Author

Gus Wiseman, Jan 27 2019

Status

approved