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%I #15 Aug 31 2023 15:08:18
%S 0,0,1,0,2,2,0,3,6,3,0,4,15,12,4,0,5,40,48,20,5,0,6,140,304,120,30,6,
%T 0,7,924,6080,1720,255,42,7,0,8,24640,1484736,186620,7480,483,56,8,0,
%U 9,12415040,61235956672,1393267596,3504380,26404,840,72,9,0,10
%N Table read by descending antidiagonals where T(n,k) = T(n,k-1) + T(n,k-1)^2/k^2 and T(n,0)=n.
%C Not always an integer.
%F T(n, k) = T(n, k-1) + A061315(n, k)^2.
%e The table begins:
%e 0, 0, 0, 0, 0,...
%e 1, 2, 3, 4, 5,...
%e 2, 6, 15, 40, 140,...
%e 3, 12, 48, 304, 6080,...
%e 4, 20, 120, 1720, 186620,...
%e 5, 30, 255, 7480, 3504380,...
%e 6, 42, 483, 26404, 43599605,...
%e 7, 56, 840, 79240, 392515340,...
%e 8, 72, 1368, 209304, 2738219580,...
%e ...
%Y Rows include A000004, A000027 and A061322. Columns include A001477, A002378, A061316, A061318 and A061320.
%K nonn,tabl
%O 0,5
%A _Henry Bottomley_, Apr 24 2001