A323775 - OEIS

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A323775

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

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

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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