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!)
 A008300 Triangle read by rows: T(n,k) (n >= 0, 0 <= k <= n) gives number of {0,1} n X n matrices with all row and column sums equal to k. 24
 1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 24, 90, 24, 1, 1, 120, 2040, 2040, 120, 1, 1, 720, 67950, 297200, 67950, 720, 1, 1, 5040, 3110940, 68938800, 68938800, 3110940, 5040, 1, 1, 40320, 187530840, 24046189440, 116963796250, 24046189440, 187530840, 40320, 1, 1, 362880, 14398171200, 12025780892160, 315031400802720, 315031400802720, 12025780892160, 14398171200, 362880, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Or, triangle of multipermutation numbers T(n,k), n >= 0, 0 <= k <= n: number of relations on an n-set such that all vertical sections and all horizontal sections have k elements. REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 236, P(n,k). LINKS Brendan D. McKay, Rows n = 0..30, flattened C. J. Everett and P. R. Stein, The asymptotic number of integer stochastic matrices, Disc. Math. 1 (1971), 55-72. Richard J. Mathar, 2-regular Digraphs of the Lovelock Lagrangian, arXiv:1903.12477 [math.GM], 2019. B. D. McKay, Applications of a technique for labeled enumeration, Congress. Numerantium, 40 (1983), 207-221. Brendan D. McKay, first 30 rows : entries named Bv[n,k,n,k] Wouter Meeussen, relevant entries from B. D. McKay reference FORMULA Comtet quotes Everett and Stein as showing that T(n,k) ~ (kn)!(k!)^(-2n) exp( -(k-1)^2/2 ) for fixed k as n -> oo. T(n,k) = T(n,n-k). EXAMPLE Triangle begins: 1; 1,    1; 1,    2,       1; 1,    6,       6,        1; 1,   24,      90,       24,        1; 1,  120,    2040,     2040,      120,       1; 1,  720,   67950,   297200,    67950,     720,    1; 1, 5040, 3110940, 68938800, 68938800, 3110940, 5040, 1; PROG (PARI) T(n, k)={   local(M=Map(Mat([n, 1])));   my(acc(p, v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v)));   my(recurse(i, p, v, e) = if(i<0, if(!e, acc(p, v)), my(t=polcoef(p, i)); for(j=0, min(t, e), self()(i-1, p+j*(x-1)*x^i, binomial(t, j)*v, e-j))));   for(r=1, n, my(src=Mat(M)); M=Map(); for(i=1, matsize(src)[1], recurse(k-1, src[i, 1], src[i, 2], k))); vecsum(Mat(M)[, 2]); } \\ Andrew Howroyd, Apr 03 2020 CROSSREFS Row sums give A067209. Central coefficients are A058527. Cf. A000142 (column 1), A001499 (column 2), A001501 (column 3), A058528 (column 4), A075754 (column 5), A172544 (column 6), A172541 (column 7). Cf. A133687, A333157. Sequence in context: A322620 A155795 A009963 * A321789 A173887 A288025 Adjacent sequences:  A008297 A008298 A008299 * A008301 A008302 A008303 KEYWORD tabl,nonn,nice AUTHOR EXTENSIONS More terms from Greg Kuperberg, Feb 08 2001 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 April 16 16:49 EDT 2021. Contains 343050 sequences. (Running on oeis4.)