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%I #26 Sep 22 2023 02:12:06
%S 1,2,4,11,66,1417,178803,275379307,15254411521973,
%T 108800468645440803267,964567296140908420613296779144,
%U 219614169629364529542990295052656098001967511,38626966436500261962963100479469496821891576834974275502742922521
%N Number of integer partitions of 2^n whose mean is a power of 2.
%C Number of partitions of 2^n whose number of parts is a power of 2. - _Chai Wah Wu_, Sep 21 2023
%H Chai Wah Wu, <a href="/A327484/b327484.txt">Table of n, a(n) for n = 0..15</a> (n = 0..13 from Alois P. Heinz)
%e The a(0) = 1 through a(3) = 11 partitions:
%e (1) (2) (4) (8)
%e (11) (22) (44)
%e (31) (53)
%e (1111) (62)
%e (71)
%e (2222)
%e (3221)
%e (3311)
%e (4211)
%e (5111)
%e (11111111)
%t Table[Length[Select[IntegerPartitions[2^n],IntegerQ[Mean[#]]&]],{n,0,5}]
%o (Python)
%o from sympy.utilities.iterables import partitions
%o def A327484(n): return sum(1 for s,p in partitions(1<<n,size=True) if not(s&-s)^s) # _Chai Wah Wu_, Sep 21 2023
%o (Python)
%o # uses A008284_T
%o def A327484(n): return sum(A008284_T(1<<n,1<<k) for k in range(n+1)) # _Chai Wah Wu_, Sep 21 2023
%Y Row sums of A327483.
%Y Cf. A067538, A068413, A135342, A237984, A327474, A327481, A327482.
%K nonn
%O 0,2
%A _Gus Wiseman_, Sep 13 2019
%E a(7) from _Chai Wah Wu_, Sep 14 2019
%E a(8)-a(11) from _Alois P. Heinz_, Sep 21 2023
%E a(12) from _Chai Wah Wu_, Sep 21 2023
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