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A157045 Triangular table: number of partitions of n into exactly n-k parts, each <= n-k. Same as A157044 but with rows reversed. 1

%I

%S 1,1,0,1,1,0,1,1,1,0,1,1,2,0,0,1,1,2,2,0,0,1,1,2,3,2,0,0,1,1,2,3,4,1,

%T 0,0,1,1,2,3,5,4,1,0,0,1,1,2,3,5,6,5,0,0,0,1,1,2,3,5,7,8,4,0,0,0,1,1,

%U 2,3,5,7,10,9,4,0,0,0,1,1,2,3,5,7,11,12,11,3,0,0,0,1,1,2,3,5,7,11,14,16,11

%N Triangular table: number of partitions of n into exactly n-k parts, each <= n-k. Same as A157044 but with rows reversed.

%C See A157044. Rows approach the partition numbers.

%D George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976 (Theorem 1.5).

%t Table[T[n-1,n-k,n-k+2]-T[n-1,n-k-1,n-k+2],{n,1,9},{k,1,n}] with T[n,a,b] as defined in A047993.

%Y Cf. A000041, A157044, A157046, A047993

%K nonn,tabl

%O 1,13

%A _Wouter Meeussen_, Feb 22 2009

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