cp's OEIS Frontend

A321163 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is the sum of distinct products Product_{j=1..k} b_j with 1 <= b_j<= n.

%I A321163 #29 Nov 25 2020 21:31:51
%S A321163 1,1,3,1,7,6,1,15,25,10,1,31,90,61,15,1,63,301,310,136,21,1,127,966,
%T A321163 1441,990,244,28,1,255,3025,6370,6391,2220,440,36,1,511,9330,27301,
%U A321163 38325,17731,5300,680,45,1,1023,28501,114670,218926,130851,54831,9660,1022,55
%N A321163 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is the sum of distinct products Product_{j=1..k} b_j with 1 <= b_j<= n.
%H A321163 Seiichi Manyama, <a href="/A321163/b321163.txt">Antidiagonals n = 1..25, flattened</a>
%e A321163 In case of (n,k) = (3,2):
%e A321163   | 1  2  3
%e A321163 --+--------
%e A321163 1 | 1, 2, 3
%e A321163 2 | 2, 4, 6
%e A321163 3 | 3, 6, 9
%e A321163 Distinct products are 1,2,3,4,6,9. So A(3,2) = 1+2+3+4+6+9 = 25.
%e A321163 Square array begins:
%e A321163     1,    1,     1,      1,       1,        1, ...
%e A321163     3,    7,    15,     31,      63,      127, ...
%e A321163     6,   25,    90,    301,     966,     3025, ...
%e A321163    10,   61,   310,   1441,    6370,    27301, ...
%e A321163    15,  136,   990,   6391,   38325,   218926, ...
%e A321163    21,  244,  2220,  17731,  130851,   916714, ...
%e A321163    28,  440,  5300,  54831,  514668,  4519390, ...
%e A321163    36,  680,  9660, 116991, 1280916, 13092430, ...
%e A321163    45, 1022, 17130, 242091, 3070935, 36184072, ...
%e A321163    55, 1472, 28670, 467391, 6807045, 91765822, ...
%t A321163 A[n_, k_] := Module[{b, bb}, bb = Array[b, k]; Table[Times @@ bb, Evaluate[Sequence @@ ({#, n}& /@ bb)]] // Flatten // Union // Total];
%t A321163 Table[A[n-k+1, k], {n, 1, 10}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Nov 25 2020 *)
%Y A321163 Columns 1-3 give A000217, A321165, A323334.
%Y A321163 Rows 1-2 give A000012, A000225(n+1).
%Y A321163 Main diagonal gives A321164.
%Y A321163 Cf. A322967.
%Y A321163 Row 3 gives A000392(n+4). - _Fred Daniel Kline_, Jan 11 2019
%K A321163 nonn,tabl
%O A321163 1,3
%A A321163 _Seiichi Manyama_, Jan 10 2019