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%I A323775 #6 Jan 27 2019 18:03:21
%S A323775 1,3,8,30,359,72385,4338080222,18448597098193762732,
%T A323775 340282370354622283774333836315916425069,
%U A323775 115792089237316207213755562747271079374483128445080168204415615259394085515423
%N A323775 a(n) = Sum_{k = 1...n} k^(2^(n - k)).
%C A323775 Number of ways to choose a constant integer partition of each part of a constant integer partition of 2^(n - 1).
%e A323775 The a(1) = 1 through a(4) = 30 twice-partitions:
%e A323775   (1)  (2)     (4)           (8)
%e A323775        (11)    (22)          (44)
%e A323775        (1)(1)  (1111)        (2222)
%e A323775                (2)(2)        (4)(4)
%e A323775                (11)(2)       (22)(4)
%e A323775                (2)(11)       (4)(22)
%e A323775                (11)(11)      (22)(22)
%e A323775                (1)(1)(1)(1)  (1111)(4)
%e A323775                              (4)(1111)
%e A323775                              (11111111)
%e A323775                              (1111)(22)
%e A323775                              (22)(1111)
%e A323775                              (1111)(1111)
%e A323775                              (2)(2)(2)(2)
%e A323775                              (11)(2)(2)(2)
%e A323775                              (2)(11)(2)(2)
%e A323775                              (2)(2)(11)(2)
%e A323775                              (2)(2)(2)(11)
%e A323775                              (11)(11)(2)(2)
%e A323775                              (11)(2)(11)(2)
%e A323775                              (11)(2)(2)(11)
%e A323775                              (2)(11)(11)(2)
%e A323775                              (2)(11)(2)(11)
%e A323775                              (2)(2)(11)(11)
%e A323775                              (11)(11)(11)(2)
%e A323775                              (11)(11)(2)(11)
%e A323775                              (11)(2)(11)(11)
%e A323775                              (2)(11)(11)(11)
%e A323775                              (11)(11)(11)(11)
%e A323775                              (1)(1)(1)(1)(1)(1)(1)(1)
%t A323775 Table[Sum[k^2^(n-k),{k,n}],{n,12}]
%Y A323775 Cf. A000123, A001970, A002577, A006171, A279787, A279789, A305551, A306017, A319056, A323766, A323774, A323776.
%K A323775 nonn
%O A323775 1,2
%A A323775 _Gus Wiseman_, Jan 27 2019

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