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A182930 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). 3
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, 52, 41, 877, 674, 523, 409, 322, 255, 203, 162, 4140, 3263, 2589, 2066, 1657, 1335, 1080, 877, 715, 21147, 17007, 13744, 11155, 9089, 7432, 6097, 5017, 4140, 3425 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Mirror image of A106436. - Alois P. Heinz, Jan 29 2019

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

Peter Luschny, Set partitions

FORMULA

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).

EXAMPLE

T(4,2) = card({2|134, 2|3|14, 2|4|13}) = 3.

[1]     1,

[2]     1,    0,

[3]     2,    1,    1,

[4]     5,    3,    2,    1,

[5]    15,   10,    7,    5,    4,

[6]    52,   37,   27,   20,   15,   11,

     [-1-] [-2-] [-3-] [-4-] [-5-] [-6-]

MAPLE

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:

A182930 := (n, k) -> T(n, k); seq(print(seq(A182930(n, k), k=1..n)), n=1..6);

MATHEMATICA

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]];

Table[T[n, k], {n, 1, 10}, {k, 1, n}] (* Jean-Fran├žois Alcover, Jun 22 2019 *)

CROSSREFS

Cf. A000110, A000296, A106436.

T(2n+1,n+1) gives A020556.

Sequence in context: A264698 A263296 A259862 * A232187 A076241 A316399

Adjacent sequences:  A182927 A182928 A182929 * A182931 A182932 A182933

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Apr 08 2011

STATUS

approved

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Last modified January 22 10:52 EST 2020. Contains 331144 sequences. (Running on oeis4.)