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A111377 Triangle of sum of product of partitions of n where largest part is k. 0

%I

%S 1,1,2,1,2,3,1,6,3,4,1,6,9,4,5,1,14,18,12,5,6,1,14,30,24,15,6,7,1,30,

%T 48,56,30,18,7,8,1,30,99,80,70,36,21,8,9,1,62,135,180,125,84,42,24,9,

%U 10,1,62,237,276,250,150,98,48,27,10,11,1,126,390,540,420,336,175,112,54,30

%N Triangle of sum of product of partitions of n where largest part is k.

%F T(n, k)=k*sum_j {0<=j<=k} a(n-k, j) starting with T(0, 0)=1; T(n, n)=n for n>=1.

%e Triangle starts 1; 1,2; 1,2,3; 1,6,3,4; 1,6,9,4,5; 1,14,18,12,5,6; etc.

%e T(6,3)=18 since partitions of 6 with largest part 3 is 3+3, 3+2+1, 3+1+1+1 and 3*3 + 3*2*1 + 3*1*1*1 = 18.

%Y Row sums are A006906.

%K nonn,tabl

%O 1,3

%A _Henry Bottomley_, Nov 09 2005

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