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A298484 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.

%I A298484 #33 Feb 09 2018 12:10:05
%S A298484 1,2,2,3,6,6,4,12,42,42,5,20,156,1806,1806,6,30,420,24492,3263442,
%T A298484 3263442,7,42,930,176820,599882556,10650056950806,10650056950806,8,56,
%U A298484 1806,865830,31265489220,359859081592975692,113423713055421844361000442,113423713055421844361000442
%N A298484 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 A298484 Seiichi Manyama, <a href="/A298484/b298484.txt">Antidiagonals n = 1..13, flattened</a>
%e A298484 Square array begins:
%e A298484       1,       2,         3,           4,           5,              6, ...
%e A298484       2,       6,        12,          20,          30,             42, ...
%e A298484       6,      42,       156,         420,         930,           1806, ...
%e A298484      42,    1806,     24492,      176820,      865830,        3263442, ...
%e A298484    1806, 3263442, 599882556, 31265489220, 74966245730, 10650056950806, ...
%t A298484 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 A298484 Columns k=1..3 give A007018(n-1), A007018, A004168(n-1).
%Y A298484 Rows n=1..3 give A000027, A002378, A169938.
%K A298484 nonn,tabl
%O A298484 1,2
%A A298484 _Seiichi Manyama_, Jan 20 2018