The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A331567 Array read by antidiagonals: A(n,k) is the number of binary matrices with k columns and any number of distinct nonzero rows with n ones in every column. 9
 1, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 13, 6, 0, 1, 1, 75, 120, 0, 0, 1, 1, 541, 6174, 1104, 0, 0, 1, 1, 4683, 449520, 413088, 5040, 0, 0, 1, 1, 47293, 49686726, 329520720, 18481080, 0, 0, 0, 1, 1, 545835, 7455901320, 491236986720, 179438982360, 522481680, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..209 FORMULA A(n,k) = 0 for k > 0, n > 2^(k-1). A(2^(k-1), k) = (2^k-1)! for k > 0. A331643(n) = Sum_{d|n} A(n/d, d). EXAMPLE Array begins: =============================================================== n\k | 0 1 2 3 4 5 6 ----+---------------------------------------------------------- 0 | 1 1 1 1 1 1 1 ... 1 | 1 1 3 13 75 541 4683 ... 2 | 1 0 6 120 6174 449520 49686726 ... 3 | 1 0 0 1104 413088 329520720 491236986720 ... 4 | 1 0 0 5040 18481080 179438982360 3785623968170400 ... 5 | 1 0 0 0 522481680 70302503250720 ... 6 | 1 0 0 0 7875584640 ... ... The A(2,2) = 6 matrices are: [1 1] [1 1] [1 0] [1 0] [0 1] [0 1] [1 0] [0 1] [1 1] [0 1] [1 1] [1 0] [0 1] [1 0] [0 1] [1 1] [1 0] [1 1] PROG (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)} D(p, n, k)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); WeighT(v)[n]^k/prod(i=1, #v, i^v[i]*v[i]!)} T(n, k)={ my(m=n*k+1, q=Vec(exp(intformal(O(x^m) - x^n/(1-x)))), f=Vec(serlaplace(1/(1+x) + O(x*x^m))/(x-1))); if(n==0, 1, sum(j=1, m, my(s=0); forpart(p=j, s+=(-1)^#p*D(p, n, k), [1, n]); s*sum(i=j, m, q[i-j+1]*f[i]))); } CROSSREFS Rows n=1..3 are A000670, A331640, A331641. Column k=5 is A331642. Cf. A188445, A330942, A331568, A331569, A331571, A331643. Sequence in context: A126308 A370040 A094923 * A303301 A160499 A329272 Adjacent sequences: A331564 A331565 A331566 * A331568 A331569 A331570 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Jan 20 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 13 00:40 EDT 2024. Contains 375857 sequences. (Running on oeis4.)