A333445 Table T(n,k) read by upward antidiagonals. T(n,k) = Product_{i=1..n} Sum_{j=1..k} (i-1)*k+j

1, 2, 3, 6, 21, 6, 24, 231, 90, 10, 120, 3465, 2160, 260, 15, 720, 65835, 71280, 10920, 600, 21, 5040, 1514205, 2993760, 633360, 39000, 1197, 28, 40320, 40883535, 152681760, 46868640, 3510000, 111321, 2156, 36, 362880, 1267389585, 9160905600, 4218177600

Offset

1,2

Comments

T(n,k) is the minimum value of Product_{i=1..n} Sum_{j=1..k} r[(i-1)*k+j] among all permutations r of {1..kn}. For the maximum value see A333420.

Links

Table of n, a(n) for n=1..40.

Chai Wah Wu, On rearrangement inequalities for multiple sequences, arXiv:2002.10514 [math.CO], 2020.

Formula

T(n,k) = k^(2n)*Gamma(n+(1+k)/2k)/Gamma((1+k)/2k).

Prog

(Python)
def T(n, k): # T(n, k) for A333445
    c, l = 1, 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

Sequence in context: A277876 A002078 A000372 * A123930 A238895 A125601

Adjacent sequences: A333442 A333443 A333444 * A333446 A333447 A333448

Keyword

nonn,tabl

Author

Chai Wah Wu, Mar 23 2020

Status

approved