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%I #16 Feb 26 2020 15:57:21
%S 1,1,3,15,176,6842,1505499,3913864295,338854264248680,
%T 4216199393504640098482,59475094770587936660132803278445,
%U 17618334934720173062514849536736413843694654543
%N a(n) = A000041(2^n - 1).
%C The partition numbers have an apparent fractal-like structure starting with every term in A173301.
%C Let A000041 = row 0, then under every (2^n - 1)-th term, begin a new row with the partition numbers; then take finite differences of each column from below.
%C The sum of finite difference terms will reproduce the partition numbers, with finite difference rows (starting from the top going down) = number of partitions of n that do not contain (1, 2, 3,...). (Cf. the array shown in A173302).
%D Refer to tables of the partition numbers.
%H Amiram Eldar, <a href="/A173301/b173301.txt">Table of n, a(n) for n = 0..19</a>
%F a(n) = A000041(2^n - 1), n = (0, 1, 2,...).
%F a(n) = A000041(A000225(n)). - _Omar E. Pol_, Oct 29 2013
%t Table[PartitionsP[2^n - 1], {n, 0 ,10}] (* _Amiram Eldar_, Feb 26 2020 *)
%Y Cf. A000041, A000225, A002865, A027336, A173302.
%K nonn
%O 0,3
%A _Gary W. Adamson_, Feb 15 2010
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