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A361521
Array read by descending antidiagonals. A(n, k) is the number of the nonempty multiset combinations of {0, 1} as defined in A361682.
1
0, 0, 0, 0, 2, 0, 0, 5, 4, 0, 0, 9, 12, 6, 0, 0, 14, 24, 21, 8, 0, 0, 20, 40, 45, 32, 10, 0, 0, 27, 60, 78, 72, 45, 12, 0, 0, 35, 84, 120, 128, 105, 60, 14, 0, 0, 44, 112, 171, 200, 190, 144, 77, 16, 0, 0, 54, 144, 231, 288, 300, 264, 189, 96, 18, 0
OFFSET
0,5
COMMENTS
A detailed combinatorial interpretation can be found in A361682.
FORMULA
A(n, k) = n*k*(4 + n*(k - 1))/2.
T(n, k) = k*(n - k)*(4 + k*(n - k - 1))/2.
A(n, k) = A361682(n, k) - 1.
EXAMPLE
[0] 0, 0, 0, 0, 0, 0, 0, 0, ... A000004
[1] 0, 2, 5, 9, 14, 20, 27, 35, ... A000096
[2] 0, 4, 12, 24, 40, 60, 84, 112, ... A046092
[3] 0, 6, 21, 45, 78, 120, 171, 231, ... A081266
[4] 0, 8, 32, 72, 128, 200, 288, 392, ... A139098
[5] 0, 10, 45, 105, 190, 300, 435, 595, ...
[6] 0, 12, 60, 144, 264, 420, 612, 840, ... A153792
[7] 0, 14, 77, 189, 350, 560, 819, 1127, ...
.
[0] 0;
[1] 0, 0;
[2] 0, 2, 0;
[3] 0, 5, 4, 0;
[4] 0, 9, 12, 6, 0;
[5] 0, 14, 24, 21, 8, 0;
[6] 0, 20, 40, 45, 32, 10, 0;
[7] 0, 27, 60, 78, 72, 45, 12, 0;
[8] 0, 35, 84, 120, 128, 105, 60, 14, 0;
[9] 0, 44, 112, 171, 200, 190, 144, 77, 16, 0;
MAPLE
A := (n, k) -> n*k*(4 + n*(k - 1))/2:
for n from 0 to 7 do seq(A(n, k), k = 0..7) od;
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Mar 22 2023
STATUS
approved