The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A058711 Triangle T(n,k) giving the number of loopless matroids of rank k on n labeled points (n >= 1, 1 <= k <= n). 7
 1, 1, 1, 1, 4, 1, 1, 14, 11, 1, 1, 51, 106, 26, 1, 1, 202, 1232, 642, 57, 1, 1, 876, 22172, 28367, 3592, 120, 1, 1, 4139, 803583, 8274374, 991829, 19903, 247, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS From Petros Hadjicostas, Oct 09 2019: (Start) The old references had some typos, some of which were corrected in the recent ones. Few additional typos were corrected here from the recent references. Here are some of the changes: T(5,2) = 31 --> 51; T(5,4) = 21 --> 26; sum of row n=5 is 185 (not 160 or 165); T(8,3) = 686515 --> 803583; T(8, 6) = 19904 --> 19903, and some others. This triangular array is the same as A058710 except that it has no row n = 0 and no column k = 0. (End) LINKS W. M. B. Dukes, Tables of matroids. W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000. W. M. B. Dukes, The number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004. W. M. B. Dukes, On the number of matroids on a finite set, SÃ©minaire Lotharingien de Combinatoire 51 (2004), Article B51g. FORMULA From Petros Hadjicostas, Oct 09 2019: (Start) T(n,1) = 1 for n >= 1. T(n,2) = Bell(n) - 1 = A000110(n) - 1 = A058692(n) for n >= 2. T(n,3) = Sum_{i = 3..n} Stirling2(n,i) * (A056642(i) - 1) = Sum_{i = 3..n} A008277(n,i) * A058720(i,3) for n >= 3. T(n,k) = Sum_{i = k..n} Stirling2(n,i) * A058720(i,k) for n >= k. [Dukes (2004), p. 3; see the equation with the Stirling numbers of the second kind.] (End) EXAMPLE Table T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:   1;   1,    1;   1,    4,      1;   1,   14,     11,       1;   1,   51,    106,      26,      1;   1,  202,   1232,     642,     57,     1;   1,  876,  22172,   28367,   3592,   120,   1;   1, 4139, 803583, 8274374, 991829, 19903, 247, 1;   ... CROSSREFS Same as A058710 (except for row n=0 and column k=0). Row sums give A058712. Columns include (truncated versions of) A000012 (k=1), A058692 (k=2), A058715 (k=3). Sequence in context: A267318 A050154 A179454 * A202906 A177984 A157013 Adjacent sequences:  A058708 A058709 A058710 * A058712 A058713 A058714 KEYWORD nonn,nice,tabl,more AUTHOR N. J. A. Sloane, Dec 31 2000 EXTENSIONS Several values corrected by Petros Hadjicostas, Oct 09 2019 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 00:35 EST 2020. Contains 332028 sequences. (Running on oeis4.)