This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A108458 Triangle read by rows: T(n,k) is the number of set partitions of {1,2,...,n} in which the last block is the singleton {k}, 1<=k<=n; the blocks are ordered with increasing least elements. 2
 1, 0, 1, 0, 1, 2, 0, 1, 3, 5, 0, 1, 5, 10, 15, 0, 1, 9, 22, 37, 52, 0, 1, 17, 52, 99, 151, 203, 0, 1, 33, 130, 283, 471, 674, 877, 0, 1, 65, 340, 855, 1561, 2386, 3263, 4140, 0, 1, 129, 922, 2707, 5451, 8930, 12867, 17007, 21147, 0, 1, 257, 2572, 8919, 19921, 35098, 53411, 73681, 94828, 115975 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Another way to obtain this sequence (with offset 0): Form the infinite array U(n,k) = number of labeled partitions of (n,k) into pairs (i,j), for n >= 0, k >= 0 and read it by antidiagonals. In other words, U(n,k) = number of partitions of n black objects labeled 1..n and k white objects labeled 1..k. Each block must have at least one white object. Then T(n,k)=U(n+k,k+1). Thus the two versions are related like "multichoose" to "choose". - Augustine O. Munagi, Jul 16 2007 LINKS FORMULA T(n,1)=0 for n>=2; T(n,2)=1 for n>=2; T(n,3)=1+2^(n-3) for n>=3; T(n,n)=B(n-1), T(n,n-1)=B(n-1)-B(n-2), where B(q) are the Bell numbers (A000110). Double e.g.f.: exp(exp(x)*(exp(y)-1)). U(n,k) = Sum_{i=0..k} i^(n-k)*Stirling2(k,i). - Vladeta Jovovic, Jul 12 2007 EXAMPLE Triangle T(n,k) starts: 1; 0,1; 0,1,2; 0,1,3,5; 0,1,5,10,15; T(5,3)=5 because we have 1245|3, 145|2|3, 14|25|3, 15|24|3 and 1|245|3. The arrays U(n,k) starts: 1 0 0 0 0 ... 1 1 1 1 1 ... 2 3 5 9 17 ... 5 10 22 52 130 ... 15 37 99 283 855 ... CROSSREFS Row sums of T(n, k) yield A124496(n, 1). Cf. A108461. Columns of U(n, k): A000110, A005493, A033452. Rows of U(n, k): A000007, A000012, A000051. Main diagonal: A108459. Sequence in context: A091612 A253672 A213861 * A254281 A295682 A195772 Adjacent sequences:  A108455 A108456 A108457 * A108459 A108460 A108461 KEYWORD nonn,tabl AUTHOR Christian G. Bower, Jun 03 2005; Emeric Deutsch, Nov 14 2006 EXTENSIONS Edited by N. J. A. Sloane, May 22 2008, at the suggestion of Vladeta Jovovic. This entry is a composite of two entries submitted independently by Christian G. Bower and Emeric Deutsch, with additional comments from Augustine O. Munagi. STATUS approved

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

Last modified February 19 18:21 EST 2019. Contains 320327 sequences. (Running on oeis4.)