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
Links
- Chai Wah Wu, On rearrangement inequalities for multiple sequences, arXiv:2002.10514 [math.CO], 2020.
Programs
-
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
Formula
T(n,k) = k^(2n)*Gamma(n+(1+k)/2k)/Gamma((1+k)/2k).
Comments