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%I A360335 #21 Feb 08 2023 15:15:33
%S A360335 1,1,1,1,2,1,1,3,3,1,1,3,7,5,1,1,3,12,16,8,1,1,3,15,35,38,13,1,1,3,15,
%T A360335 63,105,89,21,1,1,3,15,90,226,329,209,34,1,1,3,15,105,417,841,1014,
%U A360335 491,55,1,1,3,15,105,645,1787,3251,3116,1153,89,1
%N A360335 Array read by antidiagonals downwards: A(n,m) = number of set partitions of [2n] into 2-element subsets {i, i+k} with 1 <= k <= m.
%F A360335 A(n,m) = A001147(n) = A104443(n,2) for m >= 2n - 1.
%e A360335 Square array begins:
%e A360335   1,  1,    1,    1,     1,      1,      1,       1,       1, ...
%e A360335   1,  2,    3,    3,     3,      3,      3,       3,       3, ...
%e A360335   1,  3,    7,   12,    15,     15,     15,      15,      15, ...
%e A360335   1,  5,   16,   35,    63,     90,    105,     105,     105, ...
%e A360335   1,  8,   38,  105,   226,    417,    645,     840,     945, ...
%e A360335   1, 13,   89,  329,   841,   1787,   3348,    5445,    7665, ...
%e A360335   1, 21,  209, 1014,  3251,   7938,  16717,   31647,   53250, ...
%e A360335   1, 34,  491, 3116, 12483,  36500,  86311,  180560,  344403, ...
%e A360335   1, 55, 1153, 9610, 47481, 167631, 459803, 1062435, 2211181, ...
%e A360335   ...
%Y A360335 Main diagonal is A014307.
%Y A360335 Columns 1..4 are A000012, A000045(n+1), A052967, A320346.
%Y A360335 Cf. A001147, A104443, A360333, A360334.
%K A360335 nonn,tabl
%O A360335 1,5
%A A360335 _Peter Dolland_, Feb 03 2023

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