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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.

%I A361521 #7 Mar 23 2023 07:57:51
%S A361521 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,
%T A361521 27,60,78,72,45,12,0,0,35,84,120,128,105,60,14,0,0,44,112,171,200,190,
%U A361521 144,77,16,0,0,54,144,231,288,300,264,189,96,18,0
%N A361521 Array read by descending antidiagonals. A(n, k) is the number of the nonempty multiset combinations of {0, 1} as defined in A361682.
%C A361521 A detailed combinatorial interpretation can be found in A361682.
%F A361521 A(n, k) = n*k*(4 + n*(k - 1))/2.
%F A361521 T(n, k) = k*(n - k)*(4 + k*(n - k - 1))/2.
%F A361521 A(n, k) = A361682(n, k) - 1.
%e A361521 [0] 0,  0,  0,   0,   0,   0,   0,    0, ...  A000004
%e A361521 [1] 0,  2,  5,   9,  14,  20,  27,   35, ...  A000096
%e A361521 [2] 0,  4, 12,  24,  40,  60,  84,  112, ...  A046092
%e A361521 [3] 0,  6, 21,  45,  78, 120, 171,  231, ...  A081266
%e A361521 [4] 0,  8, 32,  72, 128, 200, 288,  392, ...  A139098
%e A361521 [5] 0, 10, 45, 105, 190, 300, 435,  595, ...
%e A361521 [6] 0, 12, 60, 144, 264, 420, 612,  840, ...  A153792
%e A361521 [7] 0, 14, 77, 189, 350, 560, 819, 1127, ...
%e A361521        | A028347 |     A163761
%e A361521      A005843  A067725
%e A361521 .
%e A361521 [0] 0;
%e A361521 [1] 0,  0;
%e A361521 [2] 0,  2,   0;
%e A361521 [3] 0,  5,   4,   0;
%e A361521 [4] 0,  9,  12,   6,   0;
%e A361521 [5] 0, 14,  24,  21,   8,   0;
%e A361521 [6] 0, 20,  40,  45,  32,  10,   0;
%e A361521 [7] 0, 27,  60,  78,  72,  45,  12,  0;
%e A361521 [8] 0, 35,  84, 120, 128, 105,  60, 14,  0;
%e A361521 [9] 0, 44, 112, 171, 200, 190, 144, 77, 16, 0;
%p A361521 A := (n, k) -> n*k*(4 + n*(k - 1))/2:
%p A361521 for n from 0 to 7 do seq(A(n, k), k = 0..7) od;
%Y A361521 Rows: A000004, A000096, A046092, A081266, A139098, A153792.
%Y A361521 Columns: A000004, A005843, A028347, A067725, A163761, A068380.
%Y A361521 Cf. A361682.
%K A361521 nonn,tabl
%O A361521 0,5
%A A361521 _Peter Luschny_, Mar 22 2023