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Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [5n] into 5-element subsets {i, i+k, i+2k, i+3k, i+4k} with 1 <= k <= m.
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%I #13 Feb 13 2023 16:15:57

%S 1,1,1,1,2,1,1,2,3,1,1,2,4,5,1,1,2,4,7,8,1,1,2,4,10,13,13,1,1,2,4,10,

%T 19,24,21,1,1,2,4,10,20,41,44,34,1,1,2,4,10,21,43,84,81,55,1,1,2,4,10,

%U 21,58,89,180,149,89,1,1,2,4,10,21,59,120,192,372,274,144,1

%N Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [5n] into 5-element subsets {i, i+k, i+2k, i+3k, i+4k} with 1 <= k <= m.

%F A(n,m) = A104431(n) = A104443(n,5) for m >= floor((5n - 1) / 4).

%e Square array begins:

%e 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e 1, 2, 2, 2, 2, 2, 2, 2, 2, ...

%e 1, 3, 4, 4, 4, 4, 4, 4, 4, ...

%e 1, 5, 7, 10, 10, 10, 10, 10, 10, ...

%e 1, 8, 13, 19, 20, 21, 21, 21, 21, ...

%e 1, 13, 24, 41, 43, 58, 59, 59, 59, ...

%e 1, 21, 44, 84, 89, 120, 124, 125, 125, ...

%e 1, 34, 81, 180, 192, 280, 289, 344, 349, ...

%e 1, 55, 149, 372, 404, 626, 648, 759, 811, ...

%e 1, 89, 274, 785, 860, 1454, 1510, 1877, 1996, ...

%e 1, 144, 504, 1637, 1816, 3272, 3414, 4263, 4565, ...

%e ...

%Y Main diagonal is A349430.

%Y Columns 1..3 are A000012, A000045(n+1), A000073(n+2).

%Y Cf. A104431, A104443, A360333..A360335, A360492, A360493.

%K nonn,tabl

%O 1,5

%A _Peter Dolland_, Feb 09 2023