The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A271466 Number T(n,k) of set partitions of [n] such that k is the largest element of the last block; triangle T(n,k), n>=1, 1<=k<=n, read by rows. 23
 1, 0, 2, 0, 1, 4, 0, 1, 4, 10, 0, 1, 6, 15, 30, 0, 1, 10, 29, 59, 104, 0, 1, 18, 63, 139, 250, 406, 0, 1, 34, 149, 365, 692, 1145, 1754, 0, 1, 66, 375, 1039, 2110, 3627, 5649, 8280, 0, 1, 130, 989, 3149, 6932, 12521, 20085, 29874, 42294, 0, 1, 258, 2703, 10039, 24190, 46299, 77133, 117488, 168509, 231950 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Each set partition is written as a sequence of blocks, ordered by the smallest elements in the blocks. LINKS Alois P. Heinz, Rows n = 1..141, flattened Wikipedia, Partition of a set FORMULA T(n,n) = 2 * A000110(n-1) = 2 * Sum_{j=0..n-1} T(n-1,j) for n>1. EXAMPLE T(1,1) = 1: 1. T(2,2) = 2: 12, 1|2. T(3,2) = 1: 13|2. T(3,3) = 4: 123, 12|3, 1|23, 1|2|3. T(4,2) = 1: 134|2. T(4,3) = 4: 124|3, 14|23, 14|2|3, 1|24|3. T(4,4) = 10: 1234, 123|4, 12|34, 12|3|4, 13|24, 13|2|4, 1|234, 1|23|4, 1|2|34, 1|2|3|4. T(5,2) = 1: 1345|2. T(5,3) = 6: 1245|3, 145|23, 145|2|3, 14|25|3, 15|24|3, 1|245|3. T(5,4) = 15: 1235|4, 125|34, 125|3|4, 12|35|4, 135|24, 135|2|4, 13|25|4, 15|234, 15|23|4, 1|235|4, 15|2|34, 1|25|34, 15|2|3|4, 1|25|3|4, 1|2|35|4. Triangle T(n,k) begins: 1; 0, 2; 0, 1, 4; 0, 1, 4, 10; 0, 1, 6, 15, 30; 0, 1, 10, 29, 59, 104; 0, 1, 18, 63, 139, 250, 406; 0, 1, 34, 149, 365, 692, 1145, 1754; 0, 1, 66, 375, 1039, 2110, 3627, 5649, 8280; 0, 1, 130, 989, 3149, 6932, 12521, 20085, 29874, 42294; ... MAPLE b:= proc(n, m, c) option remember; `if`(n=0, x^c, add( b(n-1, max(m, j), `if`(j>=m, n, c)), j=1..m+1)) end: T:= n-> (p-> seq(coeff(p, x, n-i), i=0..n-1))(b(n, 0\$2)): seq(T(n), n=1..12); MATHEMATICA b[n_, m_, c_] := b[n, m, c] = If[n == 0, x^c, Sum[b[n-1, Max[m, j], If[j >= m, n, c]], {j, 1, m+1}]]; T[n_] := Function[p, Table[Coefficient[p, x, n-i], {i, 0, n-1}]][b[n, 0, 0]]; Table[T[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, Apr 24 2016, translated from Maple *) CROSSREFS Columns k=1-10 give: A000007(n-1), A054977(n-2), A052548(n-3) for n>3, A271743, A271744, A271745, A271746, A271747, A271748, A271749. Main diagonal gives A186021(n-1). Lower diagonals d=1-10 give: A271752, A271753, A271754, A271755, A271756, A271757, A271758, A271759, A271760, A271761. Row sums give A000110. T(2n,n) gives A271467. T(2n+1,n+1) gives A271607. Cf. A095149 (k is maximum of the first block), A113547 (k is minimum of the last block). Sequence in context: A259873 A121462 A349706 * A218581 A307177 A340264 Adjacent sequences: A271463 A271464 A271465 * A271467 A271468 A271469 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Apr 08 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 05:37 EDT 2024. Contains 372807 sequences. (Running on oeis4.)