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A161051 Number of partitions of 2n into powers of two where every part appears at least twice. 1

%I

%S 0,1,1,2,1,3,2,5,3,6,5,9,6,11,9,16,11,19,16,25,19,30,25,39,30,45,39,

%T 56,45,65,56,81,65,92,81,111,92,127,111,152,127,171,152,201,171,226,

%U 201,265,226,295,265,340,295,379,340,435,379,480,435,545,480,601,545,682,601,747

%N Number of partitions of 2n into powers of two where every part appears at least twice.

%C Number of partitions of n into powers of two where every part appears at least twice (=original definition), if 2^0 is accepted as a power of two. - _R. H. Hardin_, Jul 04 2009

%H R. H. Hardin, <a href="/A161051/b161051.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: Product_{j>=1} (1 + x^(2*2^j)/(1 - x^(2^j))). - _Emeric Deutsch_, Jun 28 2009

%e a(9)=3 because we have 444222, 4422222, and 2^9. - _Emeric Deutsch_, Jun 28 2009

%p g := product(1+x^(2*2^j)/(1-x^(2^j)), j = 1 .. 20): gser := series(g, x = 0, 145): seq(coeff(gser, x, 2*n), n = 1 .. 69); # _Emeric Deutsch_, Jun 28 2009

%K nonn

%O 1,4

%A _R. H. Hardin_, Jun 02 2009

%E Definition corrected by _Emeric Deutsch_, Jun 28 2009

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Last modified December 6 06:19 EST 2022. Contains 358595 sequences. (Running on oeis4.)