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 A066991 Square array read by descending antidiagonals of number of ways of dividing n*k labeled items into k unlabeled orders with n items in each order. 1
 1, 1, 2, 1, 12, 6, 1, 120, 360, 24, 1, 1680, 60480, 20160, 120, 1, 30240, 19958400, 79833600, 1814400, 720, 1, 665280, 10897286400, 871782912000, 217945728000, 239500800, 5040, 1, 17297280, 8892185702400, 20274183401472000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS T(p,k) = (pk)!/k! is divisible by p^k but not p^(k+1) for p prime; e.g., T(3,4) = 3^4*11*10*8*7*5*4*2*1 = 19958400. LINKS Paolo Xausa, Table of n, a(n) for n = 1..820 (antidiagonals 1..40 of the array, flattened). FORMULA T(n,k) = (n*k)!/k!. EXAMPLE The array begins: n\k| 1 2 3 4 ... -------------------------------------------------------- 1 | 1, 1, 1, 1, ... 2 | 2, 12, 120, 1680, ... 3 | 6, 360, 60480, 19958400, ... 4 | 24, 20160, 79833600, 871782912000, ... 5 | 120, 1814400, 217945728000, 101370917007360000, ... ... MATHEMATICA Table[((n-k+1)*k)!/k!, {n, 10}, {k, n, 1, -1}] (* Paolo Xausa, Feb 19 2024 *) CROSSREFS Rows include A000012, A001813, A064350. Columns include A000142, A002674, A065961. Cf. A060538, A060539, A060540. Sequence in context: A342587 A008285 A119274 * A132875 A050139 A010255 Adjacent sequences: A066988 A066989 A066990 * A066992 A066993 A066994 KEYWORD nonn,tabl AUTHOR Henry Bottomley, Feb 01 2002 EXTENSIONS Edited by Paolo Xausa, Feb 19 2024 STATUS approved

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Last modified April 18 03:29 EDT 2024. Contains 371767 sequences. (Running on oeis4.)