login
Triangular array Q given by rows: Q(n,k) = number of partitions of n that do not contain k as an element; domain: 1 <= k <= n, n >= 1.
1

%I #12 Oct 27 2019 11:35:44

%S 0,1,1,1,2,2,2,3,4,4,2,4,5,6,6,4,6,8,9,10,10,4,8,10,12,13,14,14,7,11,

%T 15,17,19,20,21,21,8,15,19,23,25,27,28,29,29,12,20,27,31,35,37,39,40,

%U 41,41,14,26,34,41,45,49,51,53,54,55,55,21,35

%N Triangular array Q given by rows: Q(n,k) = number of partitions of n that do not contain k as an element; domain: 1 <= k <= n, n >= 1.

%F Q(n, k) = P(n+1, 1) - P(n, k), P given by A027293.

%F Q(n, k) = A000041(n) - A000041(n - k). - _Sean A. Irvine_, Oct 26 2019

%e Triangle begins:

%e 0,

%e 1, 1,

%e 1, 2, 2,

%e 2, 3, 4, 4,

%e 2, 4, 5, 6, 6,

%e ...

%Y Cf. A000041, A027293.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_