A188392 T(n,k) = number of (n*k) X k binary arrays with rows in nonincreasing order and n ones in every column.
1, 2, 1, 5, 3, 1, 15, 16, 4, 1, 52, 139, 39, 5, 1, 203, 1750, 862, 81, 6, 1, 877, 29388, 35775, 4079, 150, 7, 1, 4140, 624889, 2406208, 507549, 15791, 256, 8, 1, 21147, 16255738, 238773109, 127126912, 5442547, 52450, 410, 9, 1, 115975, 504717929, 32867762616
Offset: 1
Examples
Array begins:
========================================================================
n\k| 1 2 3 4 5 6 7 8
---+--------------------------------------------------------------------
1 | 1 2 5 15 52 203 877 4140
2 | 1 3 16 139 1750 29388 624889 16255738
3 | 1 4 39 862 35775 2406208 238773109 32867762616
4 | 1 5 81 4079 507549 127126912 55643064708 38715666455777
5 | 1 6 150 15791 5442547 4762077620 8738543204786
6 | 1 7 256 52450 46757209 135029200594
7 | 1 8 410 154279 335279744
8 | 1 9 625 411180
9 | 1 10 915
...
All solutions for 6 X 2
..1..1....1..1....1..0....1..1
..1..1....1..1....1..0....1..0
..1..0....1..1....1..0....1..0
..0..1....0..0....0..1....0..1
..0..0....0..0....0..1....0..1
..0..0....0..0....0..1....0..0
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..181 (terms 1..69 from R. H. Hardin)
Crossrefs
Programs
-
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, q=Vec(exp(O(x*x^m) + intformal((x^n-1)/(1-x)))/(1-x))); if(n==0, 1, sum(j=0, m, my(s=0); forpart(p=j, s+=D(p,n,k), [1,n]); s*q[#q-j]))} \\ Andrew Howroyd, Dec 12 2018