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 A068606 Square table by antidiagonals of T(n,k)=n*k*(n+k+1). 3
 0, 0, 0, 0, 3, 0, 0, 8, 8, 0, 0, 15, 20, 15, 0, 0, 24, 36, 36, 24, 0, 0, 35, 56, 63, 56, 35, 0, 0, 48, 80, 96, 96, 80, 48, 0, 0, 63, 108, 135, 144, 135, 108, 63, 0, 0, 80, 140, 180, 200, 200, 180, 140, 80, 0, 0, 99, 176, 231, 264, 275, 264, 231, 176, 99, 0, 0, 120, 216, 288 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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 EXAMPLE Rows start: 0,0,0,0,0,...; 0,3,8,15,24,...; 0,8,20,36,56,...; 0,15,36,63,96,...; etc. CROSSREFS Cf. A068607 for the same table as a triangle. Sequence in context: A346879 A326397 A140577 * A106153 A166244 A022001 Adjacent sequences:  A068603 A068604 A068605 * A068607 A068608 A068609 KEYWORD nonn,tabl AUTHOR Henry Bottomley, Feb 24 2002 STATUS approved

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Last modified January 22 00:08 EST 2022. Contains 350481 sequences. (Running on oeis4.)