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A085388
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First differences of n^k.
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4
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1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 6, 4, 0, 1, 4, 12, 18, 8, 0, 1, 5, 20, 48, 54, 16, 0, 1, 6, 30, 100, 192, 162, 32, 0, 1, 7, 42, 180, 500, 768, 486, 64, 0, 1, 8, 56, 294, 1080, 2500, 3072, 1458, 128, 0, 1, 9, 72, 448, 2058, 6480, 12500, 12288, 4374, 256, 0, 1, 10, 90, 648
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OFFSET
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1,8
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COMMENTS
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T(n,k) is the number of k-digit numbers in base n; n,k >= 2. - Mohammed Yaseen, Nov 11 2022
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LINKS
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FORMULA
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T(n,k) = (n-1)*n^(k-1) + 0^k/n. - Corrected by Mohammed Yaseen, Nov 11 2022
T(n,0) = 1; T(n,k) = n^k - n^(k-1) for k >= 1. - Mohammed Yaseen, Nov 11 2022
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EXAMPLE
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Rows begin
1, 0, 0, 0, 0, ...
1, 1, 2, 4, 8, ...
1, 2, 6, 18, 54, ...
1, 3, 12, 48, 192, ...
1, 4, 20, 100, 500, ...
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CROSSREFS
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Row-wise binomial transform is A083064.
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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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