A375099 - OEIS

%I #14 Aug 02 2024 17:40:48

%S 1,1,1,2,3,6,12,26,57,141,333,885,2259,6391,17302,51685,147937,460561,

%T 1389093,4504136,14127767,47719998,155559696,542178148,1835105103,

%U 6600158865,23035501468,85428655084,307266398440,1168951871972,4331125790382,16897269822235

%N Number of partitions of [n] into blocks whose element sum is <= n.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%e a(0) = 1: the empty partition.

%e a(1) = 1: 1.

%e a(2) = 1: 1|2.

%e a(3) = 2: 12|3, 1|2|3.

%e a(4) = 3: 12|3|4, 13|2|4, 1|2|3|4.

%e a(5) = 6: 12|3|4|5, 13|2|4|5, 14|23|5, 1|23|4|5, 14|2|3|5, 1|2|3|4|5.

%e a(6) = 12: 123|4|5|6, 12|3|4|5|6, 13|24|5|6, 13|2|4|5|6, 14|23|5|6, 15|23|4|6, 1|23|4|5|6, 14|2|3|5|6, 15|24|3|6, 1|24|3|5|6, 15|2|3|4|6, 1|2|3|4|5|6.

%Y Main diagonal of A374932.

%Y Row sums of A375023.

%Y Cf. A000110, A369079.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Jul 29 2024