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%I #18 Jun 22 2019 09:20:45
%S 1,1,0,2,1,1,5,3,2,1,15,10,7,5,4,52,37,27,20,15,11,203,151,114,87,67,
%T 52,41,877,674,523,409,322,255,203,162,4140,3263,2589,2066,1657,1335,
%U 1080,877,715,21147,17007,13744,11155,9089,7432,6097,5017,4140,3425
%N Triangle read by rows: Number of set partitions of {1,2,..,n} such that |k| is a block and no block |m| with m < k exists, (1 <= n, 1 <= k <= n).
%C Mirror image of A106436. - _Alois P. Heinz_, Jan 29 2019
%H Alois P. Heinz, <a href="/A182930/b182930.txt">Rows n = 1..141, flattened</a>
%H Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/SetPartitions">Set partitions</a>
%F Recursion: The value of T(n,k) is, if n < 0 or k < 0 or k > n undefined, else if n = 1 then 1 else if k = n then T(n-1,1) - T(n-1,n-1); in all other cases T(n,k) = T(n,k+1) + T(n-1,k).
%e T(4,2) = card({2|134, 2|3|14, 2|4|13}) = 3.
%e [1] 1,
%e [2] 1, 0,
%e [3] 2, 1, 1,
%e [4] 5, 3, 2, 1,
%e [5] 15, 10, 7, 5, 4,
%e [6] 52, 37, 27, 20, 15, 11,
%e [-1-] [-2-] [-3-] [-4-] [-5-] [-6-]
%p T := proc(n, k) option remember; if n = 1 then 1 elif n = k then T(n-1,1) - T(n-1,n-1) else T(n-1,k) + T(n, k+1) fi end:
%p A182930 := (n,k) -> T(n,k); seq(print(seq(A182930(n,k),k=1..n)),n=1..6);
%t T[n_, k_] := T[n, k] = Which[n == 1, 1, n == k, T[n-1, 1] - T[n-1, n-1], True, T[n-1, k] + T[n, k+1]];
%t Table[T[n, k], {n, 1, 10}, {k, 1, n}] (* _Jean-François Alcover_, Jun 22 2019 *)
%Y Cf. A000110, A000296, A106436.
%Y T(2n+1,n+1) gives A020556.
%K nonn,tabl
%O 1,4
%A _Peter Luschny_, Apr 08 2011
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