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 A331889 Table T(n,k) read by upward antidiagonals. T(n,k) is the minimum value of Sum_{i=1..n} Product_{j=1..k} r[(i-1)*k+j] among all permutations r of {1..kn}. 3
 1, 3, 2, 6, 10, 6, 10, 28, 54, 24, 15, 60, 214, 402, 120, 21, 110, 594, 2348, 3810, 720, 28, 182, 1334, 8556, 32808, 43776, 5040, 36, 280, 2614 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS k    1   2     3     4     5     6     7     8      9      10       11        12   --------------------------------------------------------------------------------- n  1|   1   2     6    24   120   720  5040 40320 362880 3628800 39916800 479001600    2|   3  10    54   402  3810 43776    3|   6  28   214  2348 32808    4|  10  60   594  8556    5|  15 110  1334    6|  21 182  2614    7|  28 280    8|  36 408    9|  45 570   10|  55 770 LINKS C. W. Wu, On rearrangement inequalities for multiple sequences, arXiv:2002.10514 [math.CO], 2020. FORMULA T(n,k) >= ceiling(n*((kn)!)^(1/n)). T(n,1) = n*(n+1)/2 = A000217(n). T(1,k) = k! = A000142(k). T(n,3) = A072368(n). T(n,2) = n*(n+1)*(2*n+1)/3 = A006331(n). PROG (Python) from itertools import combinations, permutations from sympy import factorial def T(n, k): # T(n, k) for A331889     if k == 1:         return n*(n+1)//2     if n == 1:         return int(factorial(k))     if k == 2:         return n*(n+1)*(2*n+1)//3     nk = n*k     nktuple = tuple(range(1, nk+1))     nkset = set(nktuple)     count = int(factorial(nk))     for firsttuple in combinations(nktuple, n):         nexttupleset = nkset-set(firsttuple)         for s in permutations(sorted(nexttupleset), nk-2*n):             llist = sorted(nexttupleset-set(s), reverse=True)             t = list(firsttuple)             for i in range(0, k-2):                 itn = i*n                 for j in range(n):                         t[j] *= s[itn+j]             t.sort()             v = 0             for i in range(n):                 v += llist[i]*t[i]             if v < count:                 count = v     return count CROSSREFS Cf. A000142, A000217, A006331, A072368. Sequence in context: A072765 A210756 A210748 * A109876 A108284 A095011 Adjacent sequences:  A331886 A331887 A331888 * A331890 A331891 A331892 KEYWORD nonn,more,tabl AUTHOR Chai Wah Wu, Mar 20 2020 STATUS approved

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)