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%I #28 Aug 29 2016 05:59:25
%S 0,1,2,4,8,14,24,41,66,105,165,253,383,574,847,1238,1794,2573,3660,
%T 5170,7245,10087,13959,19196,26252,35717,48342,65121,87331,116600,
%U 155038,205343,270928,356169,466610,609237,792906,1028764,1330772,1716486,2207851
%N Bisection (odd part) of number of partitions that do not contain 1 as a part A002865.
%C a(n+1) = number of partitions p of 2n such that (number of parts of p) is a part of p, for n >=0. - _Clark Kimberling_, Mar 02 2014
%H Alois P. Heinz, <a href="/A182747/b182747.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = p(2*n+1)-p(2*n), where p is the partition function, A000041. - _George Beck_, Aug 14 2011
%p b:= proc(n,i) option remember;
%p if n<0 then 0
%p elif n=0 then 1
%p elif i<2 then 0
%p else b(n, i-1) +b(n-i, i)
%p fi
%p end:
%p a:= n-> b(2*n+1, 2*n+1):
%p seq(a(n), n=0..40); # _Alois P. Heinz_, Dec 01 2010
%t f[n_] := Table[PartitionsP[2 k + 1] - PartitionsP[2 k], {k, 0, n}] (* _George Beck_, Aug 14 2011 *)
%t (* also *)
%t Table[Count[IntegerPartitions[2 n], p_ /; MemberQ[p, Length[p]]], {n, 20}] (* _Clark Kimberling_, Mar 02 2014 *)
%t b[n_, i_] := b[n, i] = Which[n<0, 0, n == 0, 1, i<2, 0, True, b[n, i-1] + b[n-i, i]]; a[n_] := b[2*n+1, 2*n+1]; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Aug 29 2016, after _Alois P. Heinz_ *)
%Y Cf. A000041, A002865, A058695, A135010, A138121, A182740, A182742, A182743, A182746.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Dec 01 2010
%E More terms from _Alois P. Heinz_, Dec 01 2010
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