A361521 Array read by descending antidiagonals. A(n, k) is the number of the nonempty multiset combinations of {0, 1} as defined in A361682.

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.

Links

Table of n, a(n) for n=0..65.

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, ...
       | A028347 |     A163761
     A005843  A067725
.
[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;

Crossrefs

Rows: A000004, A000096, A046092, A081266, A139098, A153792.

Columns: A000004, A005843, A028347, A067725, A163761, A068380.

Cf. A361682.

Sequence in context: A370065 A324040 A340116 * A223705 A358304 A285192

Adjacent sequences: A361518 A361519 A361520 * A361522 A361523 A361524

Keyword

nonn,tabl

Author

Peter Luschny, Mar 22 2023

Status

approved