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%I #29 May 18 2020 06:38:30
%S 1,1,0,1,2,2,2,3,4,5,6,7,9,11,13,16,19,22,27,32,37,44,52,60,70,82,95,
%T 110,127,146,169,194,221,254,291,331,377,429,487,553,626,707,800,903,
%U 1016,1145,1288,1445,1622,1819,2036,2278,2546,2842,3172,3536,3936,4381
%N Number of partitions of n into distinct parts, none being 2.
%C With offset 2 (and a(0)=a(1)=0) the number of 2's in all partitions of n into distinct parts. [_Joerg Arndt_, Feb 20 2014]
%H Vincenzo Librandi, <a href="/A015744/b015744.txt">Table of n, a(n) for n = 0..1000</a>
%H Cristina Ballantine, Mircea Merca, <a href="https://doi.org/10.26493/1855-3974.1782.127">On identities of Watson type</a>, Ars Mathematica Contemporanea (2019) Vol. 17, 277-290.
%F G.f.: (1+x)*product(j>=3, 1+x^j ). - _Emeric Deutsch_, Apr 09 2006
%F a(n+2)=sum_{k=1..floor(n/2)} (-1)^(k-1)*A000009(n-2*k). - _Mircea Merca_, Feb 20 2014
%F a(n) ~ exp(Pi*sqrt(n/3)) / (8*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Oct 30 2015
%e a(8)=4 because we have [8],[7,1],[5,3] and [4,3,1].
%p g:=(1+x)*product(1+x^j,j=3..80): gser:=series(g,x=0,70): seq(coeff(gser,x,n),n=0..57); # _Emeric Deutsch_, Apr 09 2006
%t CoefficientList[Series[Product[1+q^n, {n, 1, 60}]/(1+q^2), {q, 0, 60}], q]
%t Table[Count[Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], x_ /; ! MemberQ[x, 2]], {n, 0, 57}] (* _Robert Price_, May 17 2020 *)
%Y Cf. A025147, A015745, A015746, A015750, A015753, A015754, A015755.
%K nonn
%O 0,5
%A _Clark Kimberling_
%E Corrected and extended by _Dean Hickerson_, Oct 10, 2001
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