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A051683
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Triangle read by rows: T(n,k) = n!*k.
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18
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1, 2, 4, 6, 12, 18, 24, 48, 72, 96, 120, 240, 360, 480, 600, 720, 1440, 2160, 2880, 3600, 4320, 5040, 10080, 15120, 20160, 25200, 30240, 35280, 40320, 80640, 120960, 161280, 201600, 241920, 282240, 322560, 362880, 725760, 1088640, 1451520, 1814400, 2177280, 2540160, 2903040, 3265920
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OFFSET
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1,2
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COMMENTS
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When the numbers denote finite permutations (as row numbers of A055089) these are the circular shifts to the right within an interval. The subsequence A001563 denotes the circular shifts that start with the first element. Compare A211370 for circular shifts to the left. - Tilman Piesk, Apr 29 2017
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LINKS
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FORMULA
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EXAMPLE
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Table begins
1;
2, 4;
6, 12, 18;
24, 48, 72, 96; ...
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MATHEMATICA
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PROG
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(Haskell)
a051683 n k = a051683_tabl !! (n-1) !! (k-1)
a051683_row n = a051683_tabl !! (n-1)
a051683_tabl = map fst $ iterate f ([1], 2) where
f (row, n) = (row' ++ [head row' + last row'], n + 1) where
row' = map (* n) row
(Magma) [[Factorial(n)*k: k in [1..n]]: n in [1..15]]; // Vincenzo Librandi, Jun 15 2015
(PARI) for(n=1, 10, for(k=1, n, print1(n!*k, ", "))) \\ G. C. Greubel, Mar 27 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
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STATUS
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approved
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