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%I #33 Feb 09 2018 12:10:05
%S 1,2,2,3,6,6,4,12,42,42,5,20,156,1806,1806,6,30,420,24492,3263442,
%T 3263442,7,42,930,176820,599882556,10650056950806,10650056950806,8,56,
%U 1806,865830,31265489220,359859081592975692,113423713055421844361000442,113423713055421844361000442
%N Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is defined by the following: A(1,k) = k and A(n,k) = A(n-1,k)*(A(n-1,k)+1) for n > 1.
%H Seiichi Manyama, <a href="/A298484/b298484.txt">Antidiagonals n = 1..13, flattened</a>
%e Square array begins:
%e 1, 2, 3, 4, 5, 6, ...
%e 2, 6, 12, 20, 30, 42, ...
%e 6, 42, 156, 420, 930, 1806, ...
%e 42, 1806, 24492, 176820, 865830, 3263442, ...
%e 1806, 3263442, 599882556, 31265489220, 74966245730, 10650056950806, ...
%t A[1, k_?Positive] := k; A[n_?Positive, k_?Positive] := A[n, k] = A[n - 1, k]*(A[n - 1, k] + 1); Table[A[n - k + 1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Feb 05 2018 *)
%Y Columns k=1..3 give A007018(n-1), A007018, A004168(n-1).
%Y Rows n=1..3 give A000027, A002378, A169938.
%K nonn,tabl
%O 1,2
%A _Seiichi Manyama_, Jan 20 2018
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