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A051683 Triangle read by rows: T(n,k) = n!*k. 18
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Numbers with only one nonzero digit when written in factorial base. - Franklin T. Adams-Watters, Nov 28 2011
In other words, numbers n such that A034968(n) = A099563(n). - Antti Karttunen, Jul 02 2013
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
LINKS
FORMULA
T(n,k) = A000142(A002024(n)) * A002260(n,k) = A002024(n)! * A002260(n,k) - Antti Karttunen, Jul 02 2013
EXAMPLE
Table begins
1;
2, 4;
6, 12, 18;
24, 48, 72, 96; ...
MATHEMATICA
T[n_, k_] := n!*k; Flatten[Table[T[n, k], {n, 9}, {k, n}]] (* Jean-François Alcover, Apr 22 2011 *)
PROG
(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
-- Reinhard Zumkeller, Mar 09 2012
(Scheme): (define (A051683 n) (* (A000142 (A002024 n)) (A002260 n))) -- Antti Karttunen, Jul 02 2013
(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
CROSSREFS
Cf. A000142, row sums give A001286(n+1).
Sequence in context: A181416 A225566 A273009 * A215821 A332284 A192096
KEYWORD
easy,nice,nonn,tabl
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)