OFFSET
0,3
COMMENTS
Considering partitions with up to n positive integers each no more than k (or equivalently paths of length n+k from one corner to the opposite corner of an n*k rectangle) there are C(n+k,n) such partitions (or paths); the mean of the sums of the partitions (or mean of the areas above the paths) is nk/2; and the variance of the sums of the partitions (or variance of the areas above the paths) is a(n)/12.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
EXAMPLE
0
0 3
0 8 20
0 15 36 63
0 24 56 96 144
0 35 80 135 200 275
0 48 108 180 264 360 468
0 63 140 231 336 455 588 735
0 80 176 288 416 560 720 896 1088
MATHEMATICA
Flatten[Table[n*k*(n+k+1), {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, May 17 2015 *)
CROSSREFS
KEYWORD
AUTHOR
Henry Bottomley, Feb 24 2002
STATUS
approved