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A077029
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Rectangle R(i,j) read by ascending antidiagonals: column j has j-1 zeros followed by numbers congruent to 1 mod j-1.
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1
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1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 1, 0, 0, 1, 4, 3, 0, 0, 0, 1, 5, 5, 1, 0, 0, 0, 1, 6, 7, 4, 0, 0, 0, 0, 1, 7, 9, 7, 1, 0, 0, 0, 0, 1, 8, 11, 10, 5, 0, 0, 0, 0, 0, 1, 9, 13, 13, 9, 1, 0, 0, 0, 0, 0, 1, 10, 15, 16, 13, 6, 0, 0, 0, 0, 0, 0, 1, 11, 17, 19, 17, 11, 1, 0, 0, 0, 0, 0, 0, 1, 12, 19, 22, 21, 16, 7, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,8
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COMMENTS
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The number of occurrences of k is the number of divisors of k-1, for k>=2. Column 1 of the inverse of this infinite matrix begins with (1,-1,1,-1,2,-6,24,-120,6!,-7!,8!,-9!,...). The remaining columns are likewise expressible in terms of factorials.
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LINKS
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FORMULA
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R(i, j) = (i-j)*(j-1)+1 if 1<=j<=i; R(i, j)=0 if j>=i+1.
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EXAMPLE
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Northwest corner:
1 0 0 0 0 0
1 1 0 0 0 0
1 2 1 0 0 0
1 3 3 1 0 0
1 4 5 4 1 0
1 5 7 7 5 1
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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