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A111377 Triangle of sum of product of partitions of n where largest part is k. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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: A162453 A008313 A232177 * A014046 A243919 A231775

Adjacent sequences:  A111374 A111375 A111376 * A111378 A111379 A111380

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Nov 09 2005

STATUS

approved

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Last modified February 20 22:25 EST 2018. Contains 299387 sequences. (Running on oeis4.)