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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A333901 Array read by antidiagonals: T(n,k) is the number of n X k nonnegative integer matrices with all column sums n and row sums k. 11
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 7, 7, 1, 1, 1, 1, 19, 55, 19, 1, 1, 1, 1, 51, 415, 415, 51, 1, 1, 1, 1, 141, 3391, 10147, 3391, 141, 1, 1, 1, 1, 393, 28681, 261331, 261331, 28681, 393, 1, 1, 1, 1, 1107, 248137, 7100821, 22069251, 7100821, 248137, 1107, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS T(n,k) is the number of ordered factorizations of m^n into n factors, where m is a product of exactly k distinct primes and each factor is a product of k primes (counted with multiplicity). LINKS Andrew Howroyd, Table of n, a(n) for n = 0..405 (antidiagonals n=0..27) FORMULA T(n,k) = T(k,n). EXAMPLE Array begins: ======================================================= n\k | 0 1   2     3       4          5            6 ----+--------------------------------------------------   0 | 1 1   1     1       1          1            1 ...   1 | 1 1   1     1       1          1            1 ...   2 | 1 1   3     7      19         51          141 ...   3 | 1 1   7    55     415       3391        28681 ...   4 | 1 1  19   415   10147     261331      7100821 ...   5 | 1 1  51  3391  261331   22069251   1985311701 ...   6 | 1 1 141 28681 7100821 1985311701 602351808741 ...   ... The T(3,2) = 7 matrices are:   [1 1]  [1 1]  [1 1]  [2 0]  [2 0]  [0 2]  [0 2]   [1 1]  [2 0]  [0 2]  [1 1]  [0 2]  [1 1]  [2 0]   [1 1]  [0 2]  [2 0]  [0 2]  [1 1]  [2 0]  [1 1] PROG (PARI) T(n, k)={   local(M=Map(Mat([k, 1])));   my(acc(p, v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v)));   my(recurse(h, p, q, v, e) = if(!p, if(!e, acc(q, v)), my(i=poldegree(p), t=pollead(p)); self()(n, p-t*x^i, q+t*x^i, v, e); for(m=1, h-i, for(j=1, min(t, e\m), self()(if(j==t, n, i+m-1), p-j*x^i, q+j*x^(i+m), binomial(t, j)*v, e-j*m)))));   for(r=1, n, my(src=Mat(M)); M=Map(); for(i=1, matsize(src)[1], recurse(n, src[i, 1], 0, src[i, 2], k))); vecsum(Mat(M)[, 2]) } for(n=0, 7, for(k=0, 7, print1(T(n, k), ", ")); print) CROSSREFS Columns k=0..9 are A000012, A000012, A002426, A172743, A172816, A172868, A172904, A172931, A172947, A172961. Main diagonal is A110058. Cf. A257462, A257493. Sequence in context: A147989 A119329 A334549 * A054724 A349350 A061494 Adjacent sequences:  A333898 A333899 A333900 * A333902 A333903 A333904 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Apr 18 2020 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 December 6 13:24 EST 2021. Contains 349563 sequences. (Running on oeis4.)