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

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, 48, 56, 30, 18, 7, 8, 1, 30, 99, 80, 70, 36, 21, 8, 9, 1, 62, 135, 180, 125, 84, 42, 24, 9, 10, 1, 62, 237, 276, 250, 150, 98, 48, 27, 10, 11, 1, 126, 390, 540, 420, 336, 175, 112, 54, 30

Offset

1,3

Links

Table of n, a(n) for n=1..76.

Formula

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.

Example

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

Crossrefs

Row sums are A006906.

Sequence in context: A008313 A334550 A232177 * A014046 A243919 A231775

Adjacent sequences: A111374 A111375 A111376 * A111378 A111379 A111380

Keyword

nonn,tabl

Author

Henry Bottomley, Nov 09 2005

Status

approved