A111377 - OEIS

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

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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.