cp's OEIS Frontend

A340385 Number of integer partitions of n into an odd number of parts, the greatest of which is odd.

%I A340385 #6 Jan 09 2021 08:37:32
%S A340385 1,0,2,0,3,1,6,3,10,7,18,15,30,28,51,50,82,87,134,145,211,235,331,375,
%T A340385 510,586,779,901,1172,1366,1750,2045,2581,3026,3778,4433,5476,6430,
%U A340385 7878,9246,11240,13189,15931,18670,22417,26242,31349,36646,43567,50854
%N A340385 Number of integer partitions of n into an odd number of parts, the greatest of which is odd.
%e A340385 The a(3) = 2 through a(10) = 7 partitions:
%e A340385   3     5       321   7         332     9           532
%e A340385   111   311           322       521     333         541
%e A340385         11111         331       32111   522         721
%e A340385                       511               531         32221
%e A340385                       31111             711         33211
%e A340385                       1111111           32211       52111
%e A340385                                         33111       3211111
%e A340385                                         51111
%e A340385                                         3111111
%e A340385                                         111111111
%t A340385 Table[Length[Select[IntegerPartitions[n],OddQ[Length[#]*Max[#]]&]],{n,30}]
%Y A340385 Partitions of odd length are counted by A027193, ranked by A026424.
%Y A340385 Partitions with odd maximum are counted by A027193, ranked by A244991.
%Y A340385 The Heinz numbers of these partitions are given by A340386.
%Y A340385 Other cases of odd length:
%Y A340385 - A024429 counts set partitions of odd length.
%Y A340385 - A067659 counts strict partitions of odd length.
%Y A340385 - A089677 counts ordered set partitions of odd length.
%Y A340385 - A166444 counts compositions of odd length.
%Y A340385 - A174726 counts ordered factorizations of odd length.
%Y A340385 - A332304 counts strict compositions of odd length.
%Y A340385 - A339890 counts factorizations of odd length.
%Y A340385 A000009 counts partitions into odd parts, ranked by A066208.
%Y A340385 A026804 counts partitions whose least part is odd.
%Y A340385 A058695 counts partitions of odd numbers, ranked by A300063.
%Y A340385 A072233 counts partitions by sum and length.
%Y A340385 A101707 counts partitions with odd rank.
%Y A340385 A160786 counts odd-length partitions of odd numbers, ranked by A300272.
%Y A340385 A340101 counts factorizations into odd factors.
%Y A340385 A340102 counts odd-length factorizations into odd factors.
%Y A340385 Cf. A000700, A027187, A078408, A174725, A236914.
%K A340385 nonn
%O A340385 1,3
%A A340385 _Gus Wiseman_, Jan 08 2021