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A323351 Number of ways to fill a (not necessarily square) matrix with n zeros and ones.

%I A323351 #11 May 23 2019 09:17:59
%S A323351 1,2,8,16,48,64,256,256,1024,1536,4096,4096,24576,16384,65536,131072,
%T A323351 327680,262144,1572864,1048576,6291456,8388608,16777216,16777216,
%U A323351 134217728,100663296,268435456,536870912,1610612736,1073741824,8589934592,4294967296,25769803776
%N A323351 Number of ways to fill a (not necessarily square) matrix with n zeros and ones.
%F A323351 a(n) = 2^n * A000005(n) for n > 0, a(0) = 1.
%F A323351 G.f.: 1 + Sum_{k>=1} 2^k*x^k/(1 - 2^k*x^k). - _Ilya Gutkovskiy_, May 23 2019
%e A323351 The a(3) = 16 matrices:
%e A323351   [000] [001] [010] [011] [100] [101] [110] [111]
%e A323351 .
%e A323351   [0] [0] [0] [0] [1] [1] [1] [1]
%e A323351   [0] [0] [1] [1] [0] [0] [1] [1]
%e A323351   [0] [1] [0] [1] [0] [1] [0] [1]
%t A323351 Table[2^n*DivisorSigma[0,n],{n,10}]
%o A323351 (PARI) a(n) = if (n==0, 1, 2^n*numdiv(n)); \\ _Michel Marcus_, Jan 15 2019
%Y A323351 Cf. A000005, A049311, A120733, A323295, A323300.
%K A323351 nonn
%O A323351 0,2
%A A323351 _Gus Wiseman_, Jan 15 2019