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 A333446 Table T(n,k) read by upward antidiagonals. T(n,k) = Sum_{i=1..n} Product_{j=1..k} (i-1)*k+j. 2
 1, 3, 2, 6, 14, 6, 10, 44, 126, 24, 15, 100, 630, 1704, 120, 21, 190, 1950, 13584, 30360, 720, 28, 322, 4680, 57264, 390720, 666000, 5040, 36, 504, 9576, 173544, 2251200, 14032080, 17302320, 40320, 45, 744, 17556, 428568, 8626800, 110941200, 603353520, 518958720, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS T(n,k) is the maximum value of Sum_{i=1..n} Product_{j=1..k} r[(i-1)*k+j] among all permutations r of {1..kn}. For the minimum value see A331889. LINKS Seiichi Manyama, Antidiagonals n = 1..140, flattened Chai Wah Wu, On rearrangement inequalities for multiple sequences, arXiv:2002.10514 [math.CO], 2020. FORMULA T(n,k) = Sum_{i=1..n} Gamma(ik+1)/Gamma((i-1)k+1). EXAMPLE From Seiichi Manyama, Jul 23 2020: (Start) T(3,2) = Sum_{i=1..3} Product_{j=1..2} (i-1)*2+j = 1*2 + 3*4 + 5*6 = 44. Square array begins: 1, 2, 6, 24, 120, 720, ... 3, 14, 126, 1704, 30360, 666000, ... 6, 44, 630, 13584, 390720, 14032080, ... 10, 100, 1950, 57264, 2251200, 110941200, ... 15, 190, 4680, 173544, 8626800, 538459200, ... 21, 322, 9576, 428568, 25727520, 1940869440, ... (End) PROG (Python) def T(n, k): # T(n, k) for A333446 c, l = 0, list(range(1, k*n+1, k)) lt = list(l) for i in range(n): for j in range(1, k): lt[i] *= l[i]+j c += lt[i] return c CROSSREFS Column k=1-3 give A000217, A268684, A268685(n-1). Main diagonal gives A336513. Cf. A323663, A331889, Sequence in context: A078091 A073883 A248982 * A289069 A074718 A285457 Adjacent sequences: A333443 A333444 A333445 * A333447 A333448 A333449 KEYWORD nonn,tabl AUTHOR Chai Wah Wu, Mar 23 2020 STATUS approved

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Last modified March 31 20:59 EDT 2023. Contains 361673 sequences. (Running on oeis4.)